During my nonrev days, I would respond to the "work" question by describing my non-flight-operations job function and responsibilities (to use a made-up example, I'd say something like, "I work with benefits software systems on a Hewlett-Packard 9000", not "I work for XX airlines' HR/Benefits Department".
Occasionally the conversation would meander around to some airline specific issue and I'd tell my seatmate about my affiliation.
One humorous incident I recall was a flight in First when the FA took my seatmate's order, then skipped me with a subtle "I'll be back later" gesture (I immediately understood that she was taking the rev passenger orders first). My seatmate became quite upset that she had skipped over me, and was about to get up to confront her when I told him why she had skipped me - we shared a good chuckle!