That's new then as they certainly used to be Waterloo. Likewise, Parkway definately used to display Farnborough but that might have been changed recently.
If they used false destinations on the down Poole stoppers at Waterloo, then logic suggests Hinton Admiral as that is the last station they serve where there is not a faster direct train. If you wanted to take connections into account connections, then Southampton Central would be the best choice. Other candidates could be Ashurst (Beaulieu Road for trains that stop there), Pokesdown or Parkstone.
Personally I prefer the use of announcing/displaying the trains as "stopping service to" rather than using false destinations, which cause confusion if the station PA/screens show Farnborough, yet the train PA/screens show Waterloo!
+1. All the major PIS systems are capable of it, so it's a mystery why (as far as I can tell) no TOCs use that facility. SWT experimented with it earlier this year, but that policy seems to have been mysteriously reverted now.
Surely it shouldn't be that hard for a PIS to be able to classify services automatically based on the number of stops in relation to others? Or the time to destination?
Then again, we end up with the potential for confusion when the PIS and the train's destination screens disagree: SWT have taken to displaying things like "Poole (stopping service)" or "London Waterloo (semifast)" on the 444/450s' destination blinds.
This is all well and good out at, say, Hook or Farnborough. But at Brookwood or Woking, for example, it really becomes an "express" service (semifasts stop at Weybridge etc.) Unless the Guard or Driver were to change these manually en-route, a passenger could easily get confused when the service announced as the express to Waterloo rolls up displaying "stopping service" on its destination board.