One of the other problems with native tribal names is that for a large number of tribes, their own tribal name usually equates to something like "the people", and their names for neighboring tribes (especially ones they didn't get along with) were far less flattering. And often a dominant tribe's names for people in their region is what stuck.
Example 1: The Apache. Their indigenous name for themselves is inde, "people". The word Apache is (depending on which etymology you believe), either a Zuni word for the Navajo tribe (which are a related subgroup of the Southern Athabaskan family), or a Yavapai word for "enemy".
Example 2: The Chichimeca. An indigenous group in NW Mexico, the word chichimeca comes from Nahuatl and meant "dog people", with similar connotations as the word barbaros carried in Classical Greece.
Example 3: The Zhuang. The largest of China's 55 recognized ethnic minorities (a whopping 1.2% of the population), the character originally used to write their name meant "a type of wild dog". This bit is hard to explain, but the left-hand portion of the character (which often gives you a sense of a 'category'), was the radical used for animals rather than people. In 1949, this was recognized as pejorative and replaced the animal radical with a human radical, but still kind of translated as "human+child servant". Better, but still patronizing as fuck. Finally, during a round of character simplifications in the 1970s, it was changed to a new character altogether meaning "strong".
The thing is, all three of those groups (mostly) proudly call themselves by the common appellations given to them, regardless of the original pejorative meanings. Hell, even "Yankee" was originally a pejorative used by the British against the colonials, then adopted by the colonials, then used by Southern Americans to refer to Northern Americans, and finally adopted with gusto by New York's professional baseball team.
As Lord Shonus said, probably best to let people decide what they want to be called, whether that's ethnic, political, gender orientation/identity, etc.