Going from Center to Approach, they actually use 3 letter ID's. LA Feeder Sector, for example is T2F, Norton is T3N, Palm Springs is T3S, Hemet is T3V, etc. T stands for Terminal. Or you can just hit T and the handoff will be directed to where the computer "thinks" the aircraft is supposed to be going. Normally works out great unless you are doing something weird with the aircraft, or in some instances where the route gets a little funky.
Similarly, it works the same way when handing off from Center to Center. To give a handoff to Albuquerque Sector 92, for instance, I would either use A92, or I could hit A and assuming things are going well, it will automatically flash the handoff to the appropriate Albuquerque Sector.
In house, between center sectors, it's just the two number sector number.