Sort of surprising there isn't one already. There is a TR, aka "The Big Stick".
Still I think we should go back to naming carriers after famous earlier ships. "Enterprise" goes way back, as does "Constellation", "Lexington", "Saratoga" and "United States" (there was once supposed to be a carrier, the first of a class, by that name but it got canceled. If the name weren't still in use by the original holder, the "USS Constitution" would make a great name for the next class of carriers.
There was a USS Franklin D. Roosevelt. It was CV-42, and was originally to be called the Coral Sea, but FDR dies shortly before the christening, and the Navy changed the name.
There's a USS Roosevelt now, named after FDR. It's an Arleigh Burke class destroyer, DDG-80, homeported in Mayport.