Continuity mistake: When Able screws Kryten's head on, he is standing in front of him. In the next shot, Able is behind Kryten next to the table. (00:15:30)
Revealing mistake: In the scene where Kochanski, the Cat, and Kryten first discover the time wand, there are a group of Canaries who are frozen in time from its effects. In the first shot of these people, the woman on the far right of the screen blinks her eyes. (Confirmed on DVD commentary). (00:15:50)
Visible crew/equipment: When the crocodile is thrown at Ace, the crash mat is visible as he lands. The mat disappears in later shots. (00:01:00)
Timeslides - S3-E5
Continuity mistake: When we see the photo of the skiers, there are no boxes in front of the screen. When the shot changes, two boxes have appeared which Rimmer and Lister use as steps. (00:07:20)
Stasis Leak - S2-E4
Continuity mistake: When Lister puts his hand under his arm pit, his locks move from behind his back to over his right shoulder in one cut, and then back again. (00:18:00)
Quarantine - S5-E4
Revealing mistake: When Lister uses the keypad to escape from Quarantine, more button lights turn off than he has actually pressed. (00:23:35)
Other mistake: Kryten sees Ace's ship before it materialises. (00:12:55)
Stasis Leak - S2-E4
Continuity mistake: When the Cat attacks the 'dog' in the hotel, between shots it changes position as he jumps on it. (00:22:20)
Rimmerworld - S6-E5
Revealing mistake: When Rimmer kisses the female Rimmer, the scar on his cheek disappears. (00:22:30)
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 ★