I answered this question a few years ago here. Here's a copy and paste of what I wrote, though there is more discussion and back and forth at the original link.

Linguist here who works with several different First Nations communities. The conventions for translating or not translating names into English really have no rules beyond convenience and going with what goes. As far as convenience is concerned, here's a few trends.

-- Nations with long polysynthetic meaningful names generally get their names translated. The means that almost all Cree, Ojibwa, and Sioux names seem to get translated. Think Tȟatȟáŋka Íyotake - Sitting Bull.

BUT! this doesn't seem to hold true since back in the earliest days of at least American history, many names from nations very closely related to these same nations didn't get translated. Powhatan, Pocahontas, etc. Possible (likely) differences include the fact that in the earlier times, Tribes like the Narraganset and such were considered valuable trading partners and also equally human, despite the serious differences, while during the later period of western expansion, there was a lot less respect and willingness to accommodate non-English names.

Jumping further to the Pacific Northwest, while many names are easily analyzable and translatable, there is a longstanding local tradition of generally not translating names as they are passed back and forth between language groups. Many people I know have names that are clearly from neighbouring or even more distant nations, and while they might change pronunciation, they aren't translated. This is reflected in English usage where we refer to Chief Pootlass, Chief Maquinna, and so on.

The "MEANINGFUL" part is important as well - In Cree for example (and I think in Lakota/Dakota as well) all names are meaningful, meaning that they use the same morphemes as the rest of the language. So any name can be translated, and in fact it's fairly natural to translate when speaking, given that people don't draw strong distinctions between "name language" and "normal language". In the language I'm working with now, Nuxalk, the Nuxalk root word dictionary includes several hundred names as separate entries, and it's very clear that many or most names are not immediately translatable, furthermore because of the suffixes available for creating names, multiple names exist with basically the same meaning, but pronounced different to distinguish people, so you can't simply translate all their names or you end up with a lot of confusion.

Another impact in this later period is the prevalence of residential type schools, and how common it was to give people "Christian" names, so often when people wanted to use an easy to say name, they'd go with "John" or "Herb" and so on.

This same trend played out on the prairies of Canada, where many First Nations had some European bloodlines in them, and if people needed to they could fall back on a European name to make things go smoother, and were often known by both. Many in my family had both Cree names and English names, but when one of them signed treaty six, he signed with his Cree name.

Another obvious factor is pronunciation. Some languages have tones, pops, nasals, and sound just really difficult to an English ear. So more likely to be changed.

Last factor I'll mention is the presence of trade languages or the medium of communication. In the prairies, a LOT of First Nations had access to English or French speakers from hundreds of years of trading. New people come, you can always explain your name. Other areas used pidgins like Chinook Wawa or Mobilian Jargon, and nicknames were a common part of the playfulness that tended to result from using these languages. Names like Skookum John and such that sound mixed were often Pidgin nicknames.

So in conclusion, there are a lot of different reasons: linguistic reasons, political reasons, power reasons, or simply going to the preferences of whoever first wrote the name down or how the first meeting went.

This question has already been answered extremely well. However, I figured I'd provide a book recommendation. Our Beloved Kin: A New History of King Philip’s War by Lisa Brooks does exactly what you are looking for in your question. All names in the book are written in the Wampanoag language, not the later English translations. That's where the "new history" comes in at. Essentially it's tackling King Philip's War mainly from the perspective of the tribes involved and not the English. Although it makes sense to refer to people's names in their native language, Brooks takes it a step further by also referring to places in that language. This serves a couple of purposes. It really helps show how the Wampanoag had their own world, separate from the English, that has virtually been erased over time. The second is that it's actually really disorienting. I found myself getting somewhat confused and having to make sure I knew where something was happening and who was doing it throughout the entire book. While it may sound like a negative, it's actually the same thing that the English were going through when trying to figure out what was going on. It's written to purposely be confusing in a good way and forces you to take their language seriously.

This question sounded familiar to me, and sure enough, it has been discussed before and then expanded on later by /u/Muskwatch.