Rex is the holographic owner and bartender of Rex's Bar in the Dixon Hill programme, whom Lwaxana Troi decides to marry without realising he is not real.
Rex appears in Manhunt. He runs the quiet bar in which Picard, playing Dixon Hill, takes refuge from Lwaxana Troi during the Enterprise-D's journey to the Pacifica conference. He pours drinks, listens and treats Hill as a regular.
Lwaxana, in the phase of Betazoid life in which a woman's desires greatly increase, has been looking for a husband among the crew. She tracks Picard to the holodeck with Riker and Data, but is at once taken with the bartender, whose mind she cannot read at all, a quality she finds fascinating.
She announces that she will marry Rex. Picard has to explain that he is a hologram and cannot leave the room, and she leaves the ship embarrassed, though not before exposing two Antedean delegates as assassins.