HS681 would probably have been called “Aldershot” it appears.
Names for TSR2 just don’t seem to have any foundation. They all seem to have grown from rumours and home-grown theories. The only vaguely useful detail is the plan to name the F-111K “Merlin” which might suggest that had history been different, the same name might have first been applied to TSR2.
One other interesting snippet is that “TSR2” was never a proper name for the aircraft at all, and it was simply a phrase used by the Ministry of Supply to refer to the weapons system as a whole… and subsequently became an accepted term. Technically-speaking, the aircraft remained as the “Vickers-Supermarine Type 571” throughout its short life.