In Peru, the Panacas (the "incan royal houses") who assisted the Spanish Conquistadors kept their aristocratic status in Colonial Peru. In fact, many pieces of peruvian colonial art were financed by Incan patrons, and they ended up having great pride of their ancestry.
This caste would be abolished around the late 18th century, after the Great Rebellion of Tupac Amaru, when an Incan noble who claimed descent from the last Incan ruler organized an armed rebellion to vanquish the Spaniards.
Did the spaniards recognize an Aztec (or Tlaxcala?) nobility during the colonial years? If not, why didn't this happen?
You might be interested in these answers:
What happened to the Tlaxcalans? written by u/Jolex41
Why did the "Spanish" conquest of Mexico end up that way... written by u/drylaw
Yes, they absolutely did.
Check these answers from /u/400-Rabbits, /u/Grombrindal18, and /u/Jolex41
https://www.reddit.com/r/AskHistorians/comments/449hvy/after_the_spanish_came_to_the_new_world_and/
https://www.reddit.com/r/AskHistorians/comments/6h78as/what_happened_to_the_tlaxcalans/