You have to set the FID on the Mode-S transponder to exactly the same ID as indicated in the flightplan. Otherwise a match between the flight plan data and the Mode-S radar target is not possible for ATC. This is what the ICAO rules say. The commercial flight number is of no use for ATC.
There is a supervision unit operating in Maastricht that reports Mode-S faulty IDs to the European airlines (via the local authority) and asks to stop that. Around 20-30% of all FID transmitted by Mode-S transponders do not correspond to the flight plan ID these days.
Among the most popular missettings are:
Set the IATA airline code instead of the ICAO code, but with the correct flight id to follow
Set the correct airline code but a commercial flight number iso of a differing callsign
Set no airline code, but only a flight id
Set no ID at all
Leave the last flight's ID in place
Set the registration iso of full flightplan ID
Set some mix of aircraft type, registration (popular for business jets)
Set some awkward alpha crap
It's just to take your flight plan printout and transfer the few characters to the FID window one by one and ATC will be happy.