Wheeler Peak in the Sangre de Cristo Range
New Mexico received its name long before the present-day nation of México won independence from Spain and adopted that name in 1821. Spanish explorers recorded this region as New Mexico (Nuevo México in Spanish) in 1563. In 1581, the Chamuscado and Rodríguez Expedition named the region north of the Río Grande “San Felipe del Nuevo México.” The Spaniards hoped to find wealthy Mexican Indian cultures there similar to those of the Aztec (Mexica) Empire of the Valley of México. The indigenous cultures of New Mexico, however, proved to be unrelated to the Aztecs and were not wealthy. Before statehood, the name “New Mexico” was applied to various configurations of the U.S. Territory, to a Mexican state, and to a province of New Spain, all in the same general area but of varying extensions.
From Wikipedia: https://en.wikipedia.org/wiki/New_Mexico#Etymology