Actually, they do... which is why the Florida State Seminoles get to keep their moniker. The Seminole tribe loves it.
The NCAA tried this same crap with the Seminoles a couple of years ago, and Florida State threatened to pull out of NCAA altogether (and thereby hold back the revenue). The NCAA quickly backed down and granted the Seminoles a waiver.
The BIG fish, here, though is a guy named "Ralph Engelstadt" (sp?). He's a massive donor to their sports programs, the hockey arena is named for him, and so on.
He told the university a few years ago that the money spigot shuts off if they rename their team. That was more-or-less the end of the discussion.
Good for him, sez me.