Because native americans were alive when these teams were created.
The two sports I know of regarding this question are the Redskins in the NFL and the Cleveland Indians in major league baseball. I have noticed that colleges and universities seem to be OK on this matter. St John's University changed from the RedMen to Redstorm.
The general sentiment of Native Americans is that they should not be used. The reasons will vary widely, but are expressed by some (at least) in derogatory statements of non-indian examples (not reproduced here as they are inflammatory.)
Shesely is a native American name
No, Native American's did not have or use 'last names' (Surnames) until they were forced to do so by the American Government. Since then many Native American's have adopted other names they knew, or stuck with traditional nouns (names).
I am a Native American millionaire!
ABSOLUTELY NOT! That's totally racist. After all the things that whites have done to Native Americans why do they try to "honor" them with football teams and business names? Only name the business after a Native American chief if the business supports Native Americans.
REDHORSE
um.......marco
Names can not be translated into any native American language.
English names have no meaning in any native American language.
Nika, amona,gitchi manitou, alliouya