As fedorqui has mentioned, tungsten and wolfram are the names for the same chemical element. Without repeating what he has written, but acknowledging it at the same time (and including some additional information I think would be helpful), here's my answer to your question:
English standards set
In English, tungsten is now the standard term for the element wolfram. In 2005, the International Union of Pure and Applied Chemistry (IUPAC)
... decided to use the term tungsten instead of wolfram; but "W" remains the chemical symbol of the element.
— Source: "About Tungsten," International Tungsten Industry Association
Keep in mind that IUPAC governs the naming of elements, not minerals, and that wolfram's first meaning (as listed in Merriam-Webster) is simply a variant of "wolframite" (not tungsten). Although wolframite is the main source of the metal tungsten, tungsten is an element of it, not another name for it. To make matters more confusing, wolfram can also be a synonym of the element tungsten (and not the mineral wolframite), but this is a secondary meaning. It may help to have a solid understanding of the difference between a mineral and an element. If you need a refresher, this should help.
Spanish standards set
While standards have been somewhat set into stone in English, and those countries that adhere to the standards set forth by IUPAC are likely to use "tungsten" or the equivalent word in each country's respective language, in Spanish, it doesn't appear that one single term has been decided upon. Two names for this element are recognized by the Royal Spanish Academy [Real Academia Española](RAE) (tungsteno and wolframio).
The word "volframio" is also recognized by the RAE. In fact, according to this source here, "wolframio" ...
... should be spelt with a “v” in Spanish, not with a “w”
presumably because the word Wolfram, the word from which this element's name is derived, is German and in the German language, a "w" is pronounced like a "v." Even so, it doesn't appear that this spelling convention (and other alternatives I've seen) ever became very popular.
Interestingly enough, Spain is one of the four Spanish-speaking countries affiliated with IUPAC. (The other three are Costa Rica, Peru, and Uruguay. Puerto Rico is also considered an affiliate.) Spain is affiliated with it through its Spanish Royal Society of Chemistry [Real Sociedad Española de Química (RSEQ)] and, surprisingly enough, an advanced search of its pages indicates that "wolframio" is preferred over "tungsteno" and by quite a bit (7:1). One of its publications is actually titled "Jornadas sobre Wolframio." In fact, its sequicentennial will be celebrated in Salamanca next month. You can see more details about it here.
The Centro Nacional de Alta Tecnología (CeNAT), the organization through which Costa Rica is associated with IUPAC, has both a Spanish and English version of its website, but the word "tungsten" didn't produce any results on either the English or Spanish version of its site, and neither did "wolframio." The word "wolfram" did produce two articles, but they were simply citations from www.wolfram.com, the site for the software company founded by Stephen Wolfram. Nothing showed up for searches of the Sociedad Chilena de Química, the Programa de Desarrollo de las Ciencias Básicas (PEDECIBA), or the Colegio de Químicos de Puerto Rico, the organizations through which Chile, Uruguay, and Puerto Rico, respectively, are affiliated with IUPAC.
So, as far as setting any standards with terms for chemical elements, this looks as if it is restricted to IUPAC and compliance is voluntary, but I'll say a lot more about regional usage of these terms before I finish answering your question.
For now, suffice it to say I could find no evidence that the RAE ever recognized the following as Spanish words: tungsten, volfram, vólfram. On the other hand, the following appear to have been recognized at some point in time: tungsteno, wolframio, wolfram, and volframio. And currently, the RAE recognizes these four:
tungsteno - wólfram - wolframio - volframio
although "wólfram" refers you to "wolframio" and it is mentioned that "volframio" is seldom used.
I should add that the Spanish-speaking world isn't completely devoid of attempting to set standards for scientific names. At one point in time, it appears that the word "tungsten," spelled just like the English word by the same name for the same thing was adopted by at least some in the Spanish-speaking scientific community. That's what this Google Ngram seems to indicate anyway.
And as late as 2011, "tungsten" was still in use on Spanish Wikipedia, but this was questioned by a couple of Wikipedia contributors. The solution, if you read the Spanish discussion page fedorqui referenced, was simply to rename the page "Wolframio" and now the first line of that article reads:
El wolframio o volframio, también conocido como wólfram o tungsteno, es un ...
If you read fedorqui's excerpt from the Spanish Wikipedia page carefully, though, you will notice that debates over usage went beyond "tungsten" vs. "tungsteno." Spanish members of IUPAC have been resistant to the change to "tungsten" (tungsteno) over "wolfram" (wolframio) citing the fact that, apparently, the name "wolfram" was chosen over "tungsten" at an IUPAC conference in 1949. Please see ukemi's comment below for more details (or better yet, the portion of ukemi's original answer that was ultimately edited out).
This now explains why I see so many more instances of "wolframio" than "tungsteno" from the Spanish Royal Society of Chemistry and why its upcoming conference in Salamanca will bear the name "Jornadas sobre el Wolframio."
Etymology
You didn't ask about this, but it may interest you to know a little about the history and meaning of the words "tungsten" and "wolfram." Plus, I don't think this really deserves an entirely new discussion thread, so I'm going to add a short blurb about it here. Did you know that the word "tungsten" comes from ...
... the Swedish words tung sten, which mean "heavy stone." Tungsten's chemical symbol comes from its earlier, Germanic name, Wolfram. The name Wolfram comes from the mineral wolframite, in which it was discovered. Wolframite means "the devourer of tin" since the mineral interferes with the smelting of tin.
— Source: "About Tungsten," from the series "It's Elemental," Jefferson Lab, a U.S. National laboratory located in Newport News, Virginia.
The name "tungsten" is used in ...
... English, French, and many other languages as the name of the element, but not in the Nordic countries ... "Wolfram" (or "volfram") is used in most European (especially Germanic, Spanish and Slavic) languages ...
— Source: "Tungsten," Wikipedia
The word "wolfram" comes from ...
... "wulf" (meaning "wolf") combined with "hraban" (meaning "raven") and related to the animals that accompanied the Nordic God Odin. The element tungsten's symbol (W) is from this word.
— Source: "Wolfram," Wiktionary
Back in the Middle Ages, miners started referring to an unknown substance that interfered with their tin smelting as "wolfram." This would later come to be known as ...
... "wolframite," which comes from the ...
... German "wolf rahm" ("wolf soot" or "wolf cream") [sometimes even translated as "wolf spittle"], the name given to tungsten by Johan Gottschalk Wallerius in 1747.
— Source: "Tungsten," Wikipedia
Note: Per Janus Bahs Jacquet, whose comments you can see in the comments section for this answer, the rahm in wolfrahm is actually short for Eisenrahm which means "iron froth."
Though the word "wolframite" is derived from the word "wolfram," the etymology of these two words differs and they mean slightly different things to some, but in American English, as per Merriam-Webster, "wolfram" is synonymous with "wolframite." If this only confuses you further, or if you are still wondering why there are two words for the same thing, this here will clear it up for you, quickly and clearly without being short on detail, and if you're still curious, follow the links to the newsletters. They're quite detailed and should sufficiently sate your curiosity on the history of tungsten/wolfram.
And for a cool, little video on tungsten mining (and one that might help visualize the difference between tungsten and wolfram, even though they are sometimes used synonymously), click here. The location is Spain, but no knowledge of the Spanish language is required and you'll be treated to some delightful Spanish music as you watch. The video's also got some rockin' good graphics, which I think you'll also enjoy.
Current usage
All of this may be interesting to you, but it still hasn't directly answered your question, which was basically
Are any of these words — wólfram, wolframio, volframio, tungsteno — used more often than the others in Spanish-speaking regions?
The short answer here is "yes." I've already touched on all of them to some extent. But I think we can all agree that this list has now been whittled down to "tungsteno" and "wolframio" (assuming you are interested in current day usage).
That said, you are still going to see instances of "tungsten" in publications written for a Spanish-speaking audience. In fact, you'll still see instances of it on the Spanish Wikipedia page that has now been titled "Wolframio." Most of the time, though, it appears to be a reference to a company or product with the name "tungsten" in it, but not always. Oddly enough, "tungsten" is also the nickname Prince Charles has given to the Duchess of Sussex, Meghan Markle, according to this article here.
Despite the fact that you will see instances of "tungsten," more often than not you're going to see "tungsteno" instead of any of the other variations for it, even "wolframio." If Google's Ngram viewer is any indicator, "wolfram" was actually more frequently used than "wolframio" up until about 1950. See for yourself:

That's just books, but I would imagine it would be reflective of other forms of communication as well. In the first comment made to your post, Yay breaks it down by the numbers in terms of Google hits found for each. I'm going to do the same but limit this to just "tungsteno" and "wolframio," and then break it out by communication medium — web pages of any kind, newspapers, books, scholarly articles, and pages from RSEQ — showing you just the ratios (since the numbers are likely to be too disparate to reasonably put into a chart):

Filaments made from tungsten are used in incandescent light bulbs like the ones you see in the chart. The bars you see in the chart for "wolframio" come from an image of the mineral "wolframite." In English, "wolfram" can refer to "wolframite" or the element "tungsten." In Spanish, "wolframio" is a synonym of "tungsteno." The word for "wolframite" in Spanish is "wolframita."
Regional differences
While either of those images might be helpful to you and others, it doesn't address where in the Spanish-speaking world either of these might be more frequently used. For that I turned to educalingo and its "Trends" section, which includes a map that indicates how frequent any given word is by shade of color and frequency number. What I saw there makes me think that "tungsteno" is very frequently used in Peru where its frequency score is 100 (the highest). In Spain, "wolframio" receives a score of 100. No other country receives that high of a frequency score for either of these words. (Incidentally, Peru has a frequency score of 0 for "wolframio" and Spain has a frequency score of 30 for "tungsteno.")
Apart from that, I noticed that Central America receives a score of 0 for both words and that many countries in South America (specifically, Venezuela, Ecuador, Peru, Bolivia, Chile, Paraguay, and Uruguay) have a score of 0 for "wolframio." Not knowing the accuracy of educalingo's trend map or what their methodology is, I wanted to check this against something else, so I ran a few experiments using an advanced Google search. I did not examine every country, but I did take a look at Bolivia (world's fourth largest producer of tungsten), Chile, and Mexico. Results that I found on educalingo's trend map really did seem to reflect the kind of returns (or lack thereof) I found online.
Mexico was particularly interesting in that it showed frequency for both, but 45 for "tungsteno" and 30 for "wolframio." This is significant in that IUPAC, a global organization but whose headquarters are located in the U.S., would likely have greater influence on Mexico than it would on Spain given the fact that the two countries are so close physically, have influenced one another's languages for centuries, and the U.S., by far, is Mexico's largest trading partner. All of this gives me confidence in recommending educalingo to you as a resource you can use to take a look at the regional differences there may be for any given word in a particular language. (Educalingo also offers several other languages in addition to Spanish.) If you want to check it out for yourself, here are the links to the words discussed in this section:
tungsteno
wolframio
The last resource I want to draw your attention to is this site called UK Data Explorer. Unfortunately, it only covers a portion of the world, but it's pretty cool nonetheless. Spain, as you may know, is a country with many different regions and though Spanish is spoken in all parts of the country, other languages (e.g., Basque, Catalán, Galician, ...) are spoken in certain pockets of it. The guy who created the site was going to take it offline in 2017, but due to requests from others, he kept it on. In case it goes offline some day, this is what it looks like:

Right away you should notice that it contradicts what I just mentioned about Spain, but when it comes to frequency, I trust my own findings via a Google search over Google Translate. Even so, the guy who created this had a good idea and if it should ever go offline, maybe someone who sees this can rebuild it (and add the rest of the world!).
TL;DR
- In English, the word "tungsten" was chosen over "wolfram" by a
reputable, international organization with a long history of serving
as the arbiter in determining the names of elements. This decision
was made in 2005.
- The use of "tungsten" over "wolfram" (or its foreign language equivalent) is in dispute because the same organization that decided the element should be named "tungsten" in 2005 is, allegedly, the same one that decided it should be named "wolfram" in 1949. Spanish-speaking members of IUPAC, in particular, are resistant to the latest change. It's a bit more complicated than that, though. If you'd like the details, read ukemi's original posted answer
here.
- Though "tungsten" was once an acceptable term in the Spanish-speaking
world, "tungsteno" and "wolframio" are the current day terms for the
element tungsten.
- Overall, "tungsteno" is more frequent than "wolframio." This is also
true of books and scholarly articles (with a Google Books or Google Scholar search). Their frequency is about equal in online news articles. The term "wolframio," on the other hand, is far more frequent in publications from the Spanish Royal Society of Chemistry, which is scheduled to host a conference in April 2019
celebrating 150 years of "Jornadas sobre Wolframio."
- According to educalingo, "wolframio" is more frequent in Spain; in the rest of
the Spanish-speaking world, especially Peru and many South American
countries "tungsteno" is more frequent. However, a Google search only shows more hits for "wolframio" from the country of Spain when that search is restricted to "News." (The ratio is about 2:1.)
- Little to no frequency for either "tungsteno" or "wolframio" in
Central America (according to educalingo).
A note on statistics discrepancies
While ukemi's answer is impressive (especially if you view even the portion that was ultimately edited out), I should explain what I know about our two sets of data. First of all, Google Trends measures frequency of searches, not frequency of the word itself. At least that is how I interpret information from its help page. Here's a quote that sums it up:
Explore what the world is searching for by entering a keyword or a topic in the Explore bar
but if you prefer to read the whole page and other relevant material on this tool, visit the Help page for Google Trends.
Educalingo doesn't have something like this on its site, but it does state this in its Trends section:
The map shown above gives the frequency of use of the term «tungsteno»* in the different countries.
*or whatever term it is you've searched for
Furthermore, when I mentioned that I had checked the educalingo results against what I found online, I wasn't looking for the words or phrases people use in their searches, but what is actually found on web pages. I also filtered for Spanish language. I'm not all that sure that ukemi's data pull from Google Trends restricted the search to just Spanish pages. I have a feeling it didn't, but this is probably somewhat of a moot point because it is likely that the search is filtered by country code.
After taking a glance at results for all pages, I then added "News" as a filter, in an attempt to capture what might be a more standard reflection of examples written by those who should have greater interest than most in writing accurately and according to a standard. (A lot of sloppy, careless, abbreviated writing can crop up in a Google search if efforts aren't made to filter it out and a "News" or "Books" search is one of the easiest ways to do that.)
I could have been more exhaustive in checking the results that educalingo had yielded, but since what that sample check produced was rather reflective of educalingo's results, I was satisfied after just checking results for Bolivia, Chile, and Mexico.
My curiosity about frequency by region was stoked even higher than before after seeing ukemi's map, so I decided to run a check using Spain as the test country. Without any filter other than "Spanish," and "Spain," "tungsteno" is, by far, more frequent than "wolframio," but when I filter for "News," "wolframio" is more frequent (by about 2:1).
What may be more revealing as to which word is more popular in Spain are the types of news outlets that use "tungsteno" and the type that use "wolframio":
tungsteno: Business Insider España, Europa Press, Gizmodo en Español, Vanity Fair in Spanish (the one Vanity Fair example I saw was actually a reference to Prince Charles's new nickname for the Duchess of Sussex)
wolframio: La Voz de Galicia, eldiario.es, La Gaceta de Salamanca, El Norte de Castilla, Diario Vasco, Diario de León, La Voz de Almería, La Vanguardia
I think you can see the point I'm trying to make. To be fair, La Vanguardia uses both, but appears to use "wolframio" twice as much. Other major Spanish news media outlets that use both but appear to prefer "wolframio" include:
Ratios in parentheses indicate the ratio of pages returned for "wolframio" versus "tungsteno."
Some, like El Economista (Spain), do seem to prefer "tungsteno" over "wolframio," but it is close — 53% of the total number of pages containing either "tungsteno" or "wolframio," contain "tungsteno" (and 47% "wolframio"). Conversely, El País, Spain's paper of record, favors "wolframio," but ever so slightly. Again, of the total that contain either word, 53% of its pages contain "wolframio" and the other 47% contain "tungsteno."
One more thing I should point out is something I found quite interesting. Ukemi mentions that the areas of Spain most likely to use "wolframio" are those that border Portugal. Initially I thought that the reason for this might be because of some influence Portuguese has on the Spanish language, but after reading this, I realize it might be more likely because most of Spain's mining companies are in western Spain.
Hope this was interesting, informative, and/or helpful. If nothing else, this shows that big data can be misleading. Sometimes you've got to dig into it a bit to make sense of it. Even acknowledging this, I realize my data and findings could be misleading as well because they still just scratch the surface, but I went to the very last page on a couple of these searches and the returns look pretty solid.
More important than anything is the register in which a term is used. Based on everything I've taken a look at on this topic thus far (e.g., comments in this thread, Google Trends, Google Searches, ...), it appears that it may be true that overall, in general, no matter where you are in the Spanish-speaking world, "tungsteno" may be more frequently used. Within the scientific community, however, or those who write about it, it looks as if Spain prefers "wolframio."
And lastly, since they say a picture is worth a thousand words, I'll leave you with one. I wanted to see for myself how mining companies in Spain presented themselves online. One of the first companies to surface was Saloro. Its site is available in English and Spanish. Below is a composite of its home page in those two languages:

Saloro is a subsidiary of Barruecopardo, which has embarked upon a tungsten mining project that, when completed, will account for approximately 13% of the non-Chinese global supply of tungsten concentrates. The Barruecopardo mine is a large open pit mine located in the Spanish province of Salamanca and represents one of the largest tungsten reserves in Spain.
Speaking of images, and this is important, take a look at the types of images that pull up on a search for "tungsteno" and those that pull up for a search of "wolframio." A "tungsteno" search pulls up a lot of images of the various things that can be made from tungsten or tungsten composites (e.g., tungsten steel) whereas one for "wolframio" tends to bring up more geologic images and images related to the chemical element. This appears to be slightly less true of Spain. But that's just the impression I got on first glance. A closer look reveals the following:

In addition to the novel El Tungsteno by César Vallejo, another book is responsible for the "wolframio" bar and how well it stacks up against the one for "tungsteno" (in the category "Book Covers," where it's actually taller worldwide.) It's because of the book, La Batalla del Wolframio: Estados Unidos y España de Pearl Harbor a la Guerra Fría (1941-1947), which was published in 2010. Its rank on Amazon is #129,463 (compared to the lower-ranked El Tungsteno , which comes in at #364,104) and you'll see a fair number of images with this book cover if you do an image search for "wolframio."
Basically, it looks as if where you are isn't as important as what you're talking about when it comes to using "tungsteno" and "wolframio." The word "wolframio" may be a bit more interchangeable with "tungsteno" when it comes to rings and watches and other types of products if you're in Spain, but if you're not talking about a tungsten product, and you're not a member of IUPAC or an affiliated scientific community, "wolframio" is likely the best word to use ... whether in Spain or elsewhere.