According to Sports Logos' Chris Creamer, the agreement finally specifies that the Arizona Coyotes do not have the right to remove the Sun Devils' logo. (the main team and the one that has priority on the arena)
So, during the Coyotes games, they will be able to put a small logo (of the Coyotes), but they will have to keep the Sun Devils one.
So, the logos of both teams will be at the center of the rink, next season. However, with this big control that Arizona State University will be able to exert on the arena's signage, you can guess that the Coyotes will (once again) lose a lot of money and cut themselves off from a significant source of revenue.