Why did they name New Mexico New Mexico?

Answer 1

Since the time of the Viceroyalty of New Spain present New Mexico was called Territorio de Nuevo México (literally Territory of New Mexico), and it shared its borders with Alta California (present California) and the State of Coahuila-Tejas (Present mexican states of Coahuila and Nuevo León and US state of Texas).

When Mexico lost the Mexican-American War, the US simply adapted the name to english, hence New Mexico.

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By the way, the U.S. occupation of Mexico City in the Mexican War is where those Halls of Montezuma in the Marine Hymn come from. And that's the war in which so many Tennesseans volunteered that it adopted the nickname "the Volunteer State." And the last Aztec emperor's name was really Moctezuma II, not Montezuma.

For a take on all that which includes a few of the things those ladies on guard at the Alamo in San Antonio probably wouldn't tell you, see:

http://en.wikipedia.org/wiki/Mexican%E2%80%93American_War

Most serious students of history would probably say that the above-referenced Wikipedia article doesn't put enough emphasis on a core conflict between Mexico's central government and the Texas settlers (many of them from Tennessee): Mexico had abolished slavery, and the "Texans" didn't want any of that.

Answer 2

You got it all wrong: Mexico City is in the country of Mexico, and it is the capital of such country. On the other hand, New Mexico was a territory of Mexico and was named in honor of such country.

New Mexico now is part of the United States because there was a war between Mexico and the United States from 1846 to 1848, and Mexico lost such war; as a result New Mexico became a territory of the United States and become a state in 1912.