I think that the PFAs time & effort would be better spent forging better diplomatic relations with all other aviation organisations. The suspicions & mistrust between organisations who are all in basically the same business are detrimental to a strong force to forward all our interests.
Name changing only serves to point out to the not so well informed that there is something wrong with that organisation.
An amalgamation into perhaps The General Aviation Advisory Authority, with an understanding within it that their "clientele" vary widely between wanting to fly IFR airways or light singles or Microlights or Gliders (fixed wing) or leap from hills or whatever. The main thing being we want to fly with as little beurocracy as possible, full stop.
If such an organisation existed it could have just as big a stick as the CAA & would have to be listened to.
However, Britain being as it is, flying pigs, heavy drinking & breweries spring to mind.