Every time I’ve tried to rename the project I ultimately fail though as my blueprints are still dependent on the old game name. The closest I’ve gotten was renaming the module, the game name, and pretty much everything, and thinking I had it working only to discover that the ThirdPersonBP.dll was still alive in my binaries and my uproject was still loading module ThirdPersonBP.dll.
EDIT: Simply renamed the stuff as you suggested while leaving the module the same and it appears to work fine. I just hope I can rename the module without issue in the near future.