Kirk... you are not correct in saying that callsigns vary from airport to ATCC. In fact they remain exactly the same throughout the flight from take-off to touchdown. You're confusing the flight numbers and the radio callsigns, which are two different things, and may differ as Gonzo has explained.
The callsigns and flight numbers will be the same for a particular flight every day but ATC can request a pilot to use a different callsign if confusion exists with another aircraft. One way is to get one aircraft to use its registration number, but this doesn't happen often.