Cheers James.
As it happens I eventually ended up just sticking with RAC Training Regiment. After some thought I discounted Battlegroup as I thought it sounded a little too "aggressive" as long as the Regiment was in cantonment at Bovington and I thought something like 1st Regiment, RAC might open up a can of worms from a lineage point of view.
Still intend to have the rest of the Army call it the Bovington Light Horse though...