Visible crew/equipment: When Ace Rimmer is talking to Mellie, a boom mic can be seen at the top of the screen. (00:04:05)
Continuity mistake: When Rimmer's mother is talking to him while he is hung upside down, she is stood about a foot away from him in one shot, then in the next she is about three feet away. (00:01:45)
Continuity mistake: As Ace Rimmer is leaving, the Cat priest has his arms behind his back. In the next shot they are in front of him. (00:06:10)
Continuity mistake: When Ace Rimmer is talking to the Cat as a priest, the Cat has the pipe in his mouth in one shot, then he is holding it in front of him in the next. (00:03:45)
Visible crew/equipment: When Rimmer is speaking to Lister about how Ace Rimmer got all the breaks in his life, a boom mic can be seen in the top left of the screen. (00:24:15)
Answer: Presumably he does, but it's never been used in any material related to the show. He is the only Cat left (as shown in Series 1), so even if he had once had a name, nobody would know it.
Moose