LORELAI: Well, I don’t know his name because I only knew him by his nickname . . . Uh, Shamu. We called him Shamu. He was kind of, um, a big guy in high school, but he’s slimmed down quite a bit.
Lorelai tries to find out Peyton’s name by phoning the organisers and pretending he’s an old school friend that she only knows by his nickname, Shamu. Shamu is the name given to several performing orcas at Sea World, previously discussed. It is a cruel nickname sometimes given to people perceived as being overweight, because orcas are also called killer whales (with the implication the person is as as fat as a whale). Despite the name, orcas are actually members of the dolphin family.
The Annotated Gilmore Girls 