Mr Moo doesn't actually go inside the club, as it would be too loud and crowded for him in there.
He stays outside with me (in his sling, under my coat) while I do my job (handling the will call list and guestlist). I take him home around midnight, when the will call and guestlist have gotten tiny enough that I can hand the job off to Athena.
As for the nickname, it refers to the fact that he LOVES boob. Loves it loves it loves it. Boob is the primary joy in his life. So, since I often feel like a dairy cow and he's my little calf, he became Mr Moo.