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 like Snoopy on The Charlie Brown Christmas Special while the popular "Peanuts" theme plays. When the family comes in, Santa’s Little Helper slowly stops dancing, sits on his hind legs, and barks.