As I understand it after the Spanish conquered the sister cities of Tenochtitlan-Tlatelolco they renamed them Mexico-Tenochtitlan. Then afterwards the country of Mexico was named after it. Correct?
Well, in colonial times the larger entity was called, "New Spain". Apparently, within New Spain, the term "Mexico" described a city, an intendancy, and an audiencia.
http://mapasdemexico.org/maps/newspain.html
http://upload.wikimedia.org/wikipedia/commons/c/cf/Viceroyalty_of_New_Spain_Location_1819_%28without_Philippines%29.png