One of the funniest ones that I can remember was Arrow Air at Miami. We used "Arrow" as a callsign but the FAA objected on the basis that it sounded too like "Aero" (which it does with an American accent).
So, we had a competition and the winning submission was "BIG A" for that was what was painted on the tail of all the aircraft and no one else in the world was ever going to use that callsign!
The winner, who was a 707 F/O I think, either got $100 or a "letter of thanks" from George.
Another one that I got involved with was "Watchdog". When I was "between jobs" I helped an ex-RAF mate out by flying a Do-228 out of EDI for the Scottish Fisheries Department.
We were "Watchdog Delta" regardless of who was flying the flight.