why can't the people who dislike the name just start calling it Old Main again, but the people who want to keep the name call it Tillman Hall?
Plenty of things are called two names by different people. Other examples: Lake Thurmond or Clark's Hill, cockroach or "palmetto bug," Civil War or war of northern aggression or war of southern independence, Persia or Iran? Sweet potato or yam?
Personally, I'm against renaming it, but if others would like to start calling it Old Main again, that's really fine with me. Maybe not perfect, but the bottom line is that a name is really nothing but a name and nobody can control what someone else calls something.