You can see from the official Mexican seal, that the official, modern name is spelled with an X and not a J.
Estados Unidos Mexicanos http://upload.wikimedia.org/wikipedia/commons/thumb/9/90/Seal_of_the_Government_of_Mexico.svg/200px-Seal_of_the_Government_of_Mexico.svg.png
(Source: Wikipedia)
Furthermore, from @Richard's answer to another question is this article about the use of x versus j and the change that took place.