HD you are correct, however the question the original OP asked was vague -
...Can someone please tell me where the info on your screens comes from! In particular Mode S returns with all the extra stuff...
The callsign info on an ATCOs screen comes from FP data paired to a specific squawk.
...Callsigns are set by the crew as Heathrow Director points out, however I believe these are broadcast from the aircraft not looked up by an ATC computer...
is a supposition by the OP that is not correct when talking about what an ATCO sees on his display.
Granted the OP may have been talking purely from an SBS receiver point of view... in which case this is not what an ATCO uses!
I think between all the replies all bases have been covered, and all answers were correct