It's a private organization. I don't know if they get public money ala a stadium, if so that can change things. There are rules that govern that stuff.
As for the sentiment part, it all depends on how people interpret it. Why would a team intentionally name themselves a derogatory phrase? It wouldn't sell. But they're portraying a fierceness, warrior mentality right? I may take pride in that like I know some Irish guys who took pride in ND. Would it matter if they chose a tribal name like Seminole?
Would anyone here be offended if a team was the "Darkies" or "ebonies"? What about "Massai", a warrior people in Africa?
"redbeards"? Berserkers? a Scottish warrior.
"topknots"? Samurai?
Which are offensive, and which aren't? Where's the line?