LORELAI: You named the spider Satchmo?
SOOKIE: After Jackson’s uncle.
Satchmo was the nickname of trumpeter and singer Louis Armstrong, previously mentioned. The nickname is short for “Satchelmouth”, but its origin is not known. Some say simply because of the size of Armstrong’s mouth, while a story favoured by biographers is that as a young boy in New Orleans, Armstrong would dance for pennies, collecting the coins in his mouth to prevent bigger children from taking them from him.
Jackson’s uncle was apparently named after the short form of a celebrity’s nickname in honour of Louis Armstrong.
The Annotated Gilmore Girls 