You need to open your livery’s aircraft.cfg file, and look for the field called “ATC_Airline=” You can enter that field with any callsign, including lower cases and spaces. So for example, you can set it to
ATC_Airline="New Zealand"
And the ATC will call you as New Zealand, instead of the default EN-EE-DOUBLEYOU-ZEALAND if you enter NEWZEALAND in the default callsign field.
The good thing about setting this up in the Aircraft.cfg is that it will be stored and carried over. Meaning as long as you keep the callsign field empty on the flight customisation menu, the sim will use the one in the aircraft.cfg. So when you switch to another livery for another airline, the sim will automatically switch to their respective callsign so you don’t have to manually change it every time.