it's more than just a north american thing. a peoples' name for itself (endonym) is often different from what their neighbours call them (exonym). old world example - deutsche v. germans. sometimes you come into contact with the neighbours first and the wrong name sticks.

Many of the popular names for tribes are based on what their neighbors called them. "Sioux" comes from an Anishinaabeg (Odawa-Ojibwe-Potawatomi) word, meaning "Little Snake." Native-Languages.org has a good list of autonyms and exonyms. Since many tribal autonyms mean "the people" or "the real people" (the Pawnee's autonym is "Chahiksichahiks" or "Men of Men"), the neighboring tribes aren't going to buy into that egotism so give them descriptive and occasionally insulting nicknames. For instance a band of Northern Paiute were named the "Chemehuevi" by the neighboring Mojave, which means "those that play with fish".

Most major tribal groups are made up of smaller groups and bands. Lakota and Dakota are two major linguistic groups within the "Sioux Nation." Oglala, Sans Arc, Hunkpapa, Two Kettles, Blackfeet, Brulé/Sicangu, and Miniconjou are the "Seven Council Fires" or band within the Lakota people.

Many federally recognized tribes are amending their constitutions to change the name of their tribes back to their autonyms, such as the Habematolel Pomo of Upper Lake, Match-e-be-nash-she-wish Band of Pottawatomi Indians of Michigan, the Ewiiaapaayp Band of Kumeyaay Indians, Ohkay Owingeh Pueblo (previously known as San Juan Pueblo) and Kewa Pueblo (previously known as Santo Domingo Pueblo).