It’s fine to register your works with your PRO under original title and publisher if you are pitching them through NE/RT libraries and/or direct to sup. NE/RT libraries almost always will create another registration with the re-title and themselves as the publisher.
If you are submitting to exclusive libraries, I would not do these registrations since it can be a pain for them to change the registration, especially if they maintain the original title.
All this being said, there is no real advantage to registering your tracks until you have a good reason such as being asked to by that one library mentioned earlier, having a REAL potential placement, etc. PRO’s look back 6 months or more on placements.
HTH 😀