I was under the impression that the data tag contains the full callsign, but maybe its only the 2 or 3 letter IATA/ICAO code and the controllers use another source to find out the callsign.
Generally only the 3-letter ICAO code appears on the strip. Some places print the callsign from the ICAO database on the strip as well, but others don't and rely on the controller to either remember them, or look up those they don't know in the book. No strips that I've seen have RMK data on them.
I have no idea how the system for changing these things works, but when the callsign changed, did the 3-letter ICAO code change or stay the same? If it stayed the same then the resulting confusion should have been fairly predictable...