The hamster's original name was Chuckie, until Telly discovered that his pet was pregnant in episode 3860. He decided that her full name was Chuckie Sue, although he continues to call her 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.)
Chuckie Sue's kids are named Moe, Larry, Curly (referencing The Three Stooges) & Chuckie.