In his first appearance (Episode 3852), he was just named Sparkles. Elizabeth lost him, and Telly Monster and Baby Bear found him, and named him Little Murray. When they realized that he belonged to Elizabeth, they returned him and explained that they called him Little Murray because he looked like one. Elizabeth agreed and decided to call him "Little Murray Sparkles."
Little Murray Sparkles' most recent appearances were in the Elmo's World "Bath Time" segment, where Telly sent Elmo a video e-mail showing him how cats take baths, and episode 4139's "The Adventures of Gina the Veterinarian". He also appears in The Not-Too-Late Show with Elmo as an audience member.
The puppet, or a copy of it, has appeared on Shara'a Simsim.