In any case, the spelling Méjico for the name of the country is little used in Mexico or the rest of the Spanish-speaking world today. The Real Academia Española itself recommends the spelling "México".

Does Mexico have regional accents?

As for regional Mexican accents, they vary incredibly from one region/state to another. They all have some common characteristics, because you can always tell a Mexican from a Spanish speaker from another country.

How many accents are there in Mexico?

The Mexican government recognizes 68 national languages, 63 of which are indigenous, including around 350 dialects of those languages.