If you're a history buff, you might now that the official name of our neighbors to the South is "Estados Unidos Mexicanos," or The United Mexican States. They're a federation, much like the United States. The name was adopted after their 1824 independence from Spain and was done in imitation of the USA.
The current Mexican president, Felipe Calderón announced in a press conference that he wants the country to change it's name to Mexico. He said that they didn't need to copy anyone else.
This is a pet cause for him. He first introduced a bill in 2003 when he was a congressman, but didn't get any traction. It seems like this time he might not have much luck either. He's leaving office in December and his proposal has been met with some resistance already.