First of all no one is going to announce before every game what company manufactured the HVAC equipment in the building. Your point is ridiculous. It's never going to happen. And Carrier will know that.
And even if they did, no one would care. Because HVAC systems aren't a consumer good and if there are 35,000 people at a football game there might be five people involved in the procurement of HVAC systems.
On on the procurement process, although an owner can tell the Engineer what equipment to specify or can actually buy the equipment themselves, this rarely happens and is filled with potential problems when it does. Universities generally lack the expertise to do this.
The University doesn't have a leg to stand on in this. The best they can do is buy Carrier out. If Carrier doesn't want to sell, the University will have to pound sand.
But Carrier probably will agree to some sort of arrangement. After all, the Carrier name on that building isn't all that valuable to them. But I wouldn't give it away. Like I said, if I were them I'd ask for not a penny less than the current value of the $2.4M which is $7 M.