They should make a rule that everytime someone says “THE Ohio State” (or any other team) they have to say “THE” in reference to the opposing team’s name. Maybe THE Ohio staters will hear how ridiculous they sound!
You are right.
I don’t care what they call themselves, but when you say “Jennifer Aniston”, people assume that you mean “the” Jennifer Aniston, not some other Jennifer Anniston in Arkansas or Alaska or somewhere.
So how many “Ohio States: are there out there, anyway?