I'm sure you know, but even seeing the distinction between "Classically Mexican names" and "Náhuatl names" strikes me as weird, since the place we get the word

I'm sure you know, but even seeing the distinction between "Classically Mexican names" and "Náhuatl names" strikes me as weird, since the place we get the word "Mexico" is the "Mexica" tribe that were the dominant of the three Nahua tribes that constituted the Aztec Empire on colonization.