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][1]<br>
(Source: [Wikipedia](http://en.wikipedia.org/wiki/Seal_of_the_United_Mexican_States))

Furthermore, from @Richard's [answer to another question](https://spanish.stackexchange.com/a/248/12) is [this article](http://www.babab.com/no05/expediente_x.htm) about the use of `x` versus `j` and the change that took place.

[Google ngrams](https://books.google.com/ngrams/graph?content=m%C3%A9xico%2Bmexico%2BM%C3%A9xico%2BMexico%2Cm%C3%A9jico%2Bmejico%2BM%C3%A9jico%2BMejico&year_start=1800&year_end=2008&corpus=21&smoothing=3&share=&direct_url=t1%3B%2C%28m%C3%A9xico%20%2B%20mexico%20%2B%20M%C3%A9xico%20%2B%20Mexico%29%3B%2Cc0%3B.t1%3B%2C%28m%C3%A9jico%20%2B%20mejico%20%2B%20M%C3%A9jico%20%2B%20Mejico%29%3B%2Cc0) also shows that, since roughly the mid 1850s, México has been the preferred spelling:

![enter image description here][2]


  [1]: https://upload.wikimedia.org/wikipedia/commons/thumb/9/90/Seal_of_the_Government_of_Mexico.svg/200px-Seal_of_the_Government_of_Mexico.svg.png
  [2]: https://i.sstatic.net/csGHB.png