Since I've previously mentioned my mongrel ancestry, who
didn't expect my comments::)?
Places founded by European immigrants most often have a borrowed name from their place of origin; if the native name of a lake, stream, etc., weren't kown, the same happened. Over the years, some native names have eventually been changed as non-local mapmakers and population shifts have lost the name or just reverted to the change (for instance, within the past 10 years or so the local "Tioga" River has been changed to the "Belmont" River on maps). By this trend, in New Hampshire, alone, the villiages of Pennacook, Contoocook, Conway (shortened from "Connaway" -- and the town of Soucook was long ago changed to Suncook), etc. will have to be changed; the only town in the world to have the name Henniker will have to be changed : I guess, to keep it close, we may revert it to a Jewish name like Hanukah (just for instance

).
As per sports team names, some of the problem has to do with history and personal perspective. Especially when the US occupational territory was forced westward, dehumanizing Native Americans provided an excuse, however hollow, to usurp their territory; from this came all sorts of savage stereotypes. Accordingly, some Native American groups were offended by the "tomahawk* chant" at the Atlanta Braves' baseball games. When these things happen, anti-discrimination forces have another 'cause' for which to spring into action; taken to the extreme, the lines between reverence and irreverence, between understanding and just plain ignorance, are lost. Then the ridiculous happens...

This reminds me of something that happened not long ago. Right near here is a state park called Squaw Creek, and it is famouse for its resident Bald Eagles. Well, someone felt that the name was offensive (they weren't Native American), and tried to get it changed. Well, they ended up leaving the name the same because no one was offended except for a small group of people, and the name was already widely known. Oh, BTW, for those who don't know, "squaw" is a word refering to a Native American woman. I don't know where it came from, but I didn't think it was considered offensive.
From a childhood addiction to Westerns (Cowboys & Indians) I always thought that squaw meant wife or woman in the Native American language. I realised even then that tribes very often had their own language so this might only apply to certain tribes.
Reference here:
http://www.straightdope.com/columns/000317.html*[For any who may not know: in the American territories, France and Britain -- during the "French and Indian War" -- paid Native Americans for each enemy scalp taken. A common instrument used was the tomahawk, a (usually stone) war axe]