Another question is, what tribe would Ilinois need permission from? Since there is no official Illini tribe, you will probably see some Native Americans (Indians) band together and claim to be the official Illini tribe. Why? Because there might be a windfall profit in it for the Indians.
The reason Florida State is fighting this so vigorously, is the multi-millions of dollars they make each year off the Seminole Indian brand and merchandise. And the reason the remnant of the Seminole tribe approves of the use of the Indian is purely for profit. Florida State pays a portion of all the marketing monies they make to the Seminoles. So if there was an official Illini Tribe, they could sanction Illinois' use of the name and depiction, and cut a similar deal with Illinois to share the profits.
The Native Americans say they are against the use of their images and names, unless they are sharing in the profits. Then they are all for it!
Several years ago an Indian activist stirred up a bunch of trouble for Bradley and a few other schools with Indian nicknames. The schools all made "donations" to the activist's "charity" (probably his charity benefitted his own family, etc) and he went away and left the schools alone. Legalized extortion is what I would call it. And the Florida State situation with the Seminole support is nothing more than a massive hypocrisy.