The word anasazi is Navajo for "enemy ancestors", I believe used in reference to the Hopi, so I imagine either the Navajo or the Hopi would prefer the state to be named after one or the other.
That having been said, we live in a TL with a state named "Idaho" which as far as we can tell is a literal nonsense word made up by white settlers and attributed to Native Americans, so the US naming a state Anasazi is certainly not unthinkable.
My idea behind Anasazi was that the Navajo majority was like "let's make the others feel included" (the Anasazis being an ancient civilization that birthed all the different Pueblo people including the Hopis). However you're correct that it originally means "enemy ancestors" so I'm thinking either Pueblo or Navajo would be better ...
(Also lawmakers suggested "Laramie" for the state of Lakota and the officials essentially answered "Oh yeah to reference that treaty you disrespected twice yeah that's awesome love it such a great way to start.")
I think it's important to note that Lakota, Hawai'i, Anasazi, Alaska and Sequoyah were all created in the 1940s after natives demanded to have special states carved out for them (for instance Hawai'i has three official languages: English, Hawai'ian and Japanese) so that they could avoid sinking completely into irrelevance.