(1) the preferred pronunciation (out here at least) is two syllables: in-din.
(2) “Nation” is preferable to “tribe” — when my Grandfather was born in the Choctaw Nation, “Indian Territory” was known by the residents as “the Nations”.
(3) by a large majority, we *don’t* object to names like “Washington Redskins”. Indians organize a lot of life around “tomtems”, symbolic representations.
For example, I’m a member of Raven Clan. If white people want to make Indians symbolic representations of power and courage and objects of veneration, that’s okay. Sort of a shame it didn’t happen earlier, but hell — make it up to us, visit a casino.