The hamster's original name was Chuckie, until Telly discovered that his pet was pregnant in episode 3860, following a playdate with Elizabeth's hamster, Herman. He decided that her full name was Chuckie Sue, although he continues to call her Chuckie. Chuckie Sue's kids are then named Moe, Larry, Curly (referencing The Three Stooges) & Chuckie.
When Chuckie Sue gave birth, Telly claims that that is a unique accomplishment proving the hamster's superiority during the "Greatest Pet in the World" contest; Zoe, however, claims that Rocco has fathered an entire family of pebbles.
Prior to Chuckie Sue, Telly previously owned a hamster named Sweetie Pie, show in episode 3759.