People who go to a high school have about as much interest in the name of the school as they have in the subjects being taught there. Their main interest is getting it over with and graduating. People who play on a sports team have more interest in making money than they do in what the name of the team they play on is.
The people involved in a school/team name change never held the original name sacred, and won't hold the next one sacred either. For 88 years, it never bothered anybody that the Washington Redskins were the Redskins, the name never really raised an eyebrow. Nobody paid the name much attention, then somebody whines about it and they have to make it politically correct so it no longer offends anybody (even though it never seemed to once in 88 years). They can even pick more neutral colors on their jerseys, how would their fans like a team with neutral colors and a lifeless name to go with it? It would be like playing a team called the neutered Bulldogs dressed in tiny pajamas versus the toxic, rabid, drug-fed junkyard Bulldogs.