You can get the actual codes used by GSX by looking at the SIM.CFG of any ground vehicle, like the staircase or the pushback. Look for this line:
couatl.atc_parking_codes =
For example, the one you asked for are:
Swissport = _SWP
Menzies = Menzies
Ground Force = Groundforce
Now, you can also see several codes that don't have their own separate livery. For example, if you have something like this:
couatl.atc_parking_codes = AAL, AALX, LOF
In the American Airlines livery, that doesn't mean we also have a separate "American Airlines Regional" (AALX) or an "American Connection" (LOF) livery too in GSX, just the American Airlines livery will be used by preference if your SCENERY has a parking with ANY of these code. So, it's one GSX livery, using multiple parking codes.
Other liveries have just one code, their own. Hope the explanation is clear.
