Fighting Illini is still their name
Illinois is an Indian word. Chicago is an Indian word. When I lived in Seattle (a variation of Chief Sealth's name) and the locals would complain about the Indian logos I wore there too, I would always have to remind them that I was born in a state with an Indian name, not a state named after a slaveowner. That always separated the people who knew history from the people who have it explained to them.
While we live in Seattle, my daughter (about 12 at the time, picked out a Washington Redskins shirt, because the color scheme was pretty cool and the store didn't have one in her size. That got the locals excited, too. I helps to have a sense of humor.