Its a gray area.
There are three "Indigenous American" themed names in the NFL that I can think of off of the top of my head.
They are the Washington Redskins, The Cleveland Indians, and the Atlanta Braves.
I don't see any problem with the "Atlanta Braves". That's no worse than the "Minnesota Vikings".
Naming teams after ancient warriors that may be associated with particular modern ethnic groups (Spartans, Vikings, etc) is ok.
On the other hand - way back in the late Sixties- when I was 12 and just becoming aware of the NFL-it was also the era of the civil rights movement. I was already wincing at the "old fashionedness" of the name of my city's team. I remember thinking about how here Martin Luther King is imploring us to judge folks by the content of their character and not...and here we have a team with skin color right in it's name!
Even then I felt that they could keep the Indian guy's profile and the tomahawk imagery on our logo, but wished that they could change the name to "the Washington Warriors" say.
I agree that "the Indians" is not as bad as "the Redskins", but it's worse than "the Braves".
One could counter that "the Cleveland Indians" is no different than "the Montreal Canadiens", "the Boston Celtics", or "Notre Dames' Fighting Irish".
Maybe. Maybe not.
Problem one: all three of those teams named after European descent ethnic groups were founded by folks who actually were of those ethnic groups, and represent cities largely populated by folks of the said ethnic group: the first being French Canadians, the other two being American descendants of Irish immigrants (a subset of the Celts). Not so the "Indians".
Problem two: peaches to pears. French Canadians, and Irish, are equivalent to...Navajos, Iroquois, or to Aztecs. Specific ethnic groups. Not to the entire race of people who populated pre Columbian north and south america, known as "Indians". The equivalent to "Indians" would be "White Folks", or "the Yellow Perils", or "the Black Africans". Names like that, which would be problematic to say the least I would think.