This is unfortunately not something you can do from within EditVoicepack yet. It is on my "things I should do" list, but unfortunately I am not having a lot of time these days, as I am preparing to sell my apartment.
When you open a "missing telephony designator" node EditVoicepack will display the path to the folder containing the aircraft.cfg file. Click this path to open an Explorer window. Now open aircraft.cfg in notepad and go to the [fltsim.X] section indicated in EditVoicepack. Now find the ATC_AIRLINE= line and change the value to the callsign you want to use.
Notice there is nothing special related to EditVoicepack here - the changes are the same you would make without EditVoicepack, you just have a lot more options for callsigns with EditVoicepack. The ATC related data in the file hasn't changed since FS2004 either, so for details I recommend you take a look at this page:http://woodair.net/Flight_Sim/tutorial/FST_CFG.htm