The dog in The Tale of the Bunny Picnic was referred to simply as "Dog" (by the Farmer) or "the Dog" (by the bunnies) throughout the story. Though good-natured at heart, he is told to fetch bunnies for the Farmer's stew. He is not very intelligent and has a habit of confusing his body parts, referring to his brain as his elbow, his nose as his knee, and his chin as his heart.
At the end of the story, the bunnies decide he needs a real name. Be-Bop names him De-Dop-De-Diddly-Dog Bop.
This puppet would appear in several future Henson projects, usually in group shots. It was repurposed as Undercover Rover in Muppet Time and played minor roles in Kermit's Swamp Years, The Muppets at Walt Disney World, and "Secrets of the Muppets." The design was used as Hugo the stunt dog from The Shaggy Dog, in Episode 19 of From the Balcony.