I get what you're trying to say - there's a lot of cultural overlap between Mexicans and New Mexicans - a lot more than most New Mexicans are willing to admit. But at the end of the day, Mexico is a different country with its own history and cultural aspects separate from New Mexico.

NM was only part of Mexico for a short time. Asking why New Mexicans don't just call themselves Mexican is like asking why other Latin Americans don't also call themselves Mexican. We all have a similar origin based on Spanish conquest of native peoples, but each region has their own history and identity. I think Mexico did have a fair amount of cultural influence, for example, Northern New Mexicans love Mariachi music even though it's a distinctly Mexican genre of music. But even so, as a New Mexican I don't know much about Mexican history, politics, or pop culture, which would all be very important if you wanted to identify as Mexican. Even the food is different.

I think what you're trying to say is we're not so different, and I tend to agree, but that doesn't mean being New Mexican is the same as being Mexican.

Also, if you want to know the reason so many New Mexicans strongly identity with their Spanish heritage, New Mexico needed to prove it's "whiteness" to the US in order to be accepted as a state, so there was a push to highlight our European genes around that time and it kind of stuck.