Kind of. The Spanish named New Mexico in the 1600s, and it was a much larger territory than the current state. The Mexicans named Mexico in 1821 when they gained their independence from Spain, and they acquired New Mexico as well. Then the US annexed it in the late 1800s.
Yes, US annexed New Mexico and Texas, which originally belonged to Mexico.
And California…
Kind of. The Spanish named New Mexico in the 1600s, and it was a much larger territory than the current state. The Mexicans named Mexico in 1821 when they gained their independence from Spain, and they acquired New Mexico as well. Then the US annexed it in the late 1800s.
https://en.m.wikipedia.org/wiki/New_Mexico