The overseas displays I was lucky enough to do used a mix of callsigns. We always used RAFAIR during the transit (they did once try to make us use the dreadful ASCOT prefix!). But once at the venue it was often agreed to use the standard UK callsign.
I guess for a solo display you can use any callsign from an ATC perspective, but if you have a multiple-aircraft display then with so many internal calls, its only going to work if you use your normal callsign.