The title of this article is a conjectural. Though the topic is found within The Simpsons universe, a proper name is not available.
The Dancing Santa's Little Helper couch gag is the fifth couch gag of Season 12.
Santa’s Little Helper dances on his hind legs a la Snoopy while a tune that's very similar to the Peanuts theme plays. When the family comes in, Santa’s Little Helper slowly stops dancing, sits on his hind legs, and barks.