I have seen this too, and can help you "fix" it.
Basically after the rename when you close the project, you most likely said save all VIs, so it resaved to disk the original Test A VIs. So go to the DQMH modules folder and look and you will see the Test A.vi and the Test A Argument -- cluster ctrl.
The error is because VIs with that name already exist on disk. So simply delete the the old, no longer used VIs. Then reopen the project and you should be good to now create Test A again.