Continuity mistake: When Legion brings the feast, Kryten is stood by the door. Rimmer says about how he appreciates art, then in the next shot of the Cat, Kryten walks behind him. Kryten would have had to walk past Rimmer in the previous shot to get there yet we did not see him while Rimmer was talking. (00:13:15)
Revealing mistake: When Lister and the Cat drop the gravestone and break their feet, you can see that it does not land anywhere near Lister's left foot. (00:26:55)
Revealing mistake: When Rimmer puts the engaged blindfold on and sits on the toilet, he doesn't take his trousers down. (00:03:50)
Revealing mistake: Holly's night cap is in front of the edges of his monitor. It should fade into the white border of his screen. (00:05:25)
Timeslides - S3-E5
Continuity mistake: When we see the skiers, no one is standing in front of the screen. In the next shot, Lister has appeared from nowhere. (00:07:20)
Continuity mistake: When Hollister picks up the lemon drink, his left hand is by his side. In the next shot it is on his chest. (00:01:50)
Revealing mistake: When Kochanski is shot with the spear, the padding that gives the impression the spear is through her leg is visibly bulging in her trousers as ahe pulls on the rope. (00:26:50)
Continuity mistake: When Lister crushes the high Rimmer's light bee, he puts his arm into Rimmer's chest. In the next shot, Lister's arm is gone. (00:21:35)
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