The Mexica existed long before the Spanish arrived. They migrated to the Valley of Mexico from a land in the north they referred to as Aztlán when the Toltecs went into decline.
Nuevo Mexico was named by the Spanish in reference to this history, as they were following the Rio Grande north searching for the Cities of Gold referenced in these same Mexica (ie Aztec) legends.
Spaniards named New Mexico a couple centuries before Mexico existed.
https://en.m.wikipedia.org/wiki/New_Mexico
The Mexica existed long before the Spanish arrived. They migrated to the Valley of Mexico from a land in the north they referred to as Aztlán when the Toltecs went into decline.
Nuevo Mexico was named by the Spanish in reference to this history, as they were following the Rio Grande north searching for the Cities of Gold referenced in these same Mexica (ie Aztec) legends.