A lavender Muppet rabbit received the name Rodney from the Amazing Mumford in episode 4270 of Sesame Street, where he's frequently seen popping out of the magician's hat.
The rabbit also appeared in a prominent speaking role (performed by Ryan Dillon) in an online video with Elmo about practicing. Here, the character is simply referred to as "Rabbit."
He also appeared in a Super Grover 2.0 segment (played by Joey Mazzarino) as one of the several woodland animals throwing a party. (First: Episode 4507)
Matt Vogel played the rabbit in a sketch where Elmo and Abby Cadabby try to find out what's hopping in Abby's picnic basket. (YouTube)
In a 2011 Nightline segment on Being Elmo, Kevin Clash put on the puppet as a demonstration while in the Muppet Workshop.
Rodney visually resembles a small lavender Anything Muppet, but with larger hands and a prominent muzzle.