Poodle is a character. He is voiced by Rodger Bumpass. He is a poodle like Lucille.
It is possible that he and Pekingese might be a gay couple because after Bletch declared to him and the other chorus members that the show will go on, Poodle reaches out and kisses Pekingese. They were also seen talking to each other in the bathroom, and when Sid comes in and accidently urinates on both of them, Poodle openly expresses his displeasure, stating that he's suppose to be on stage in five minutes.