This is an interesting topic. As said previously you have to go back many years to understand the naming of the JAR. Rhodes deserves very little credit for it. He only agreed to support it when he learned his name may go on the arena. Previously the university was under much pressure to name it after former Zip star athlete, coach and AD Kenneth "Red" Cochrane. Rhodes saw himself as a great builder and he wanted his name on as many projects as possible because he thought that would cement his legacy for decades to come in the state of Ohio. Remember the JAR was originally to seat 10,000. It's budgeting was cut twice as seats decreased. The only way it got thru the state legislature was because the architect, who was horrible, added three classrooms, at the direction of UA, so the building could then claim an educational mission. To uninformed legislators on the state capital budget committee that sounded easier to swallow than a new gym.
The whole project was a lesson in incompetence on UA's part. A few years later both Cleveland State and Wright State got their arenas funded by the legislature. Both seat near 13,000. Both are strictly for sports and campus activities. Both got neat $30,000,000 each. We got less than $10,000,000 originally with a second funding of a few million. Akron could have, and should have, done better.
Rhodes was a dynamic governor, but one who made poor decisions at times. His worst decision was to send in untrained, scared national guard troops to Kent State under an incompetent leader, General Del Corso. The results were tragic as we all know. Personally, I'd change the name in a heartbeat.