What did spain call mexico during the reign?

Spain calls Mexico New Spain because it was a Spanish colony, and depended on the reign of Spain, was controlled by the Spanish authority during 400 years. Even the southern United States was part of New Spain in these centuries (from 1500 to 1800), before the independence of Texas and the independence of Mexico. In addition, the Spanish king was in charge of appointing the viceroy in the New Spain and the Spaniards born in the new territories were called Criollos.

can someone just answer this