Strictly speaking, the reg's (sorry, no time to hunt them down) require you to use the aircraft reg, type, or ICAO-approved callsign, ONLY. Although you might get away with making up a callsign for a while, and using it, you would be breaching this legislation. Sometimes, in the past, it was possible to make local arrangements with an ATCU - I did this for a survey contract which had unusual requirements, and agreed with the local (big) radar unit that we would be such-and-such, every day. This worked well, until I called LATCC once for a 121.5 comms check, and the unusual nature of our callsign left them wondering what we were up to...
Regarding controllers knowing the callsign word, TD&H is right only in a limited sense. Most large ATCCs have the callsign word printed in small characters above the callsign on the Flight Progress Strip, so BA012 would have SPEEDBIRD printed above the BA012. Of course, most callsigns end up being committed to memory...