If no one changes their names in the first place, nothing would happen. No one would feel the urge to change their name. You can just keep the names the same and don't worry about the names.
It's not stereotyping, it is just showing off the amazing mascot that they have. They aren't going to take a picture of a real native american and use that as their logo, t hey want to make their picture really cool.
19ajones, there are teams and mascots all over the world that are like animals or something like that, it wouldn't be any different than being called the Redskins or something like that.
I think that the schools mascots shouldn't have to change, because the schools mascot could reflect on the town's history and it symbolizes the pride and the spirit of the town and school.