I don’t think many people, even some native people, are aware that the legal names of many tribes are actually not from the tribe.
Often the names came about because colonizers would ask one tribe "hey, what do you call those people over there?". then they would assign the name given to that tribe. so often the names were descriptions from unrelated tribes, or in more extreme cases, insults.
The Muscogee tribe got pretty lucky since the legal name was "creek" and it came from a different tribe going "oh, those are the people near the creek". which, is accurate enough, most creek settlements were placed along creeks. a famous one that is related to the Muscogee is the name "Cherokee". "Cherokee" is a Muscogee word meaning something along the lines of "people who don’t speak our language". Even this is pretty light compared to some names. some official tribal names translate to phrases like "dog eaters" or "lazy people".
This is why it’s not uncommon for tribes to start using older names. Muscogee comes from the term for our people "Mvskoke", and the tribe has made efforts to distance itself from the name "Creek". Although it is likely still the name you’ll hear most often.