There are many documents and records that shows baptisms of Natives but based on only vital records we can assume that there was not a single system to do so. I've seen in Durango for example in the earliest records a widow by the name Roxas who had quite a bit of slaves and servants, two generations later the last name Roxas is found on any race in this town. (natives, africans, spanish and any mix of them)

I once read, but that was many years ago and I can't recall the source. that Spain's King and Viceroy gave instructions to give "Apellidos Castellanos" to natives which would explain at some extent why Patronymic Spanish names are widely popular even on earlier records with the some exceptions like Garcia. This could be true in some cases but definitely not a system that was followed.

In the records I myself have seen I notice that proper names where mostly based on Saints, that last names (which were almost never used by natives prior 1700's in many parts of Northern Mexico) where the customary names used for orphans in Spain; De la Cruz, De los Santos, De las Iglesias, becoming, De la Cruz, Cruz, Santos and Iglesias. I also notice in some cases that Natives change their names and last names, is not uncommon to see "Jose Rodriguez" son of "Jose Gomez".

Its rare when I see a true Native name still used on a catholic record, but there are some, not to be confused with the fact of a "revival" of names that had happened in the last half century.

All in all the reasons and cases for naming where many and not systematic. They could be based on places, employers, priests, godparents, influential people, etc.

I don't think there is explicit records staying why the natives were given some specific name other than the most famous, but I believe that some ecclesiastic documents may show at some point some "advice" for the process, usually given to the priest.