score:4
I finally found this question addressed in Timothy Anna's Forging Mexico (Nebraska, 1998), pp. 36-40.
Tenochtitlán dominated the center of Mesoamerica for a century before the arrival of Spaniards, who chose the same location for their own capital. In Mexico "the hegemony of the metropolitan, urban center existed all through the colonial period."
Over time creoles developed a national identity based on the fusion of European and indigenous elements. These elites still preferred wheat to corn, but appropriated and paid lip service to native culture by revering the Virgen de Guadalupe and the eagle on a cactus devouring a snake.
David Brading named this constructed origin myth Neo-Aztecism. In it, "the identity of the nation came to be vested in the Valley of Mexico, the capital city, the political center". To this end "nationalist mythologizers" represented the whole body politic as "subsumed under the single identity of the center". That the nation then acquired a synecdochal name referring to its capital is unsurprising.
While "América" on its own was too broad, the 1814 Constitution of Apatzingán referred to "Mexican America". Both the declaration of the Congreso de Anáhuac and the 1821 Plan de Iguala called the place "Northern America". This name was accurate but failed to serve the Neo-Aztec project.
Another name at least considered was "Anáhuac", referred to in the name of the 1813 Congreso de Anáhuac. This was another Aztec term, a broader name for the known world, thematically related but not as suited to romantic mythmaking as demonyms like "Mexico".
The Plan de Iguala also called for a "new empire" (I think the question is inaccurate on this point). This was the one soon called "the Mexican Empire" that enthroned and deposed Iturbide. The eventual republic was created with the name "United Mexican States". The short-form national name "Mexico" took longer to gain currency.
Upvote:5
Mexica is the Nahuatl or "Aztec" name for the original group of "Aztecs." Over the course of several centuries, these "Mexicans" conquered the whole Central Valley of what we now call "Mexico," thereby creating the "Aztec" empire. "Mexica" is the core of this empire.
The Spanish added chunks of modern Mexico (and central America) to the Aztec empire, which is why today's "Mexico" is larger than the original Mexica. Other names for the country like "America" were considered, but the "USA" had beaten "Mexico" to the punch. Even Spanish-speaking "South" American nations might have disputed that name.
Upvote:8
Your question appears to be based upon a false assumption:
As far back as 1590, the Theatrum Orbis Terrarum showed that the northern part of the New World was known as "America Mexicana" (Mexican America), as México City was the seat for the New Spain viceroyalty. New Spain is mistaken as the old name for México, rather than the name of a large of expanse of land which covered much of North America and included the Caribbean and the Philippines. Since New Spain wasn't actually a state or a contiguous part of land, in modern times we would thought of it as a Jurisdiction under the command of the authorities in modern Mexico City. Under the Spaniards, Mexico was both the name of the capital and its sphere of influence, most of which exists as Greater Mexico City and the State of Mexico. Some parts of Puebla, Morelos and Hidalgo were also part of Spanish-era Mexico.
A bit of research shows even earlier references to Mexico, as in Historia de las cosas mas notables, rites y costumbres, del gran Reyno de la ... (1585) (Mirror).