The callsign of an airline is the nickname the traffic controllers affectionately adopt to certain airlines. For example, Pan Am's aircraft were worldwide know by controllers as 'Clippers'. Clipper 203, Clipper 207, etc, etc...
America West's callsign is 'Cactus' given the fact that its ops are based in the desert of Phoenix, Arizona. ValuJet's callsign was 'critter' for that little airplane bug they used as their logo. Some airlines just don't have them. I don't know what AeroCaribe's callsign is - if they do have one.
Pan Am - The World's Most Experienced Airline.