It seems like a cliche that British support of certain American Indian confederations would lead to an American Indian state, when the British trampled all over American Indians in the 19th and 20th centuries, and Canadian history is proof of this. But it is true the British backed American Indians against the United States who wanted to annex their lands, and even though the US won some victories against various American Indian groups (like in modern Tennessee in the 1780s/1790s), there were great victories like the famous defeat of Arthur St. Clair. Many battles could have gone toward the American Indians.
In the long term, they'd be protectorates of British North America and would eventually be forced to admit white settlement. This would be somewhat better than what they got OTL, since here you'd have a combined white and American Indian upper class ruling over poor whites and poor Indians and also their black slaves (especially in certain areas). There'd be more of their culture and language preserved than OTL, even if everything is working for the British (and wealthy whites) first, the American Indian ruling class second, and everyone else last.
Honestly, I'd say "Indiana" is a nice name for what the British would call this protectorate. They'd certainly be involved in defeating hostile Indian chiefs and their followers, just like they were OTL in North America, not to mention in India, Africa, etc. But through divide and conquer, the British might form a few protectorates which might have their historic names (and be open for white settlement).
There was a project of Native American US state named Sequoyah, so maybe Native words may become state names ?
Regions, certainly, and hopefully more than OTL, and I don't mean the lazy way of using some ethnic group/subgroup's name (or some other group's name for that group) for a placename.
Vandalia was one, and somethng about Charlotte - there are maps out there somewhere
Those were Euroamerican creations and came from the idea that certain British royals were descendents of the Vandals. Not very relevant to American Indians.
Does anyone know why they called eastern Oklahoma Sequoyah? Was it named after the famous Cherokee?
Yep, he was the namesake for the state (along with the famous trees).