That's not the problem.
FSX doesn't directly refer to the aircraft.cfg for airline callsigns, unless the airline name was there, when the section was added.
Do the following:
Go to C:/Users/*Your user/AppData/Roaming/Microsoft/FSX/SimObjects
Locate the plane in question, and open the state.cfg file in that folder.
If ie. you're trying to add an airline to [fltsim.6] in the aircraft.cfg, find the [fltsim.6] part in the state.cfg.
It should look something like this, and if it doesn't, add what's missing:
[FltSim.6]
atc_id=(the id, like OY-AVT)
atc_id_enable=1(must be set to one, shouldn't be a problem)
atc_airline=(enter a valid airline here, there's a list of the names to put there somewhere)
atc_flight_number=(your flight number)
The parenthesises are just to show what to put there.
The state.cfg files will also be able to tell you, for how long each engine of a given aircraft has been turned on, as a pointer towards your number of flighthours in that specific aircraft.
BTW, I'm not sure if you can leave out the airline in the aircraft.cfg, but put it there as well to be sure

Keep in mind, this won't add the airline to the list you can choose from in FSX, but ATC will refer to the airline name you entered.
