LORELAI: What was your girlfriend’s name, Sissy?
LUKE: As a matter of fact, no.
Lorelai teasingly suggests a girlfriend whose name is the opposite of “butch” – a “sissy”, slang for an effeminate man. There’s probably a bit of homophobic humour to Lorelai’s joke.
Lorelai had a friend in high school of this name – “Crazy Sissy”, who talked to her stuffed animals. Sissy has already been on the show as a high school girlfriend – she’s the girl Tristan took to the winter dance at Chilton, because Rory turned him down.
Note that Luke lets Lorelai know that he did have a girlfriend in high school, but he’s not saying her name. As they both went to Stars Hollow High, there’s a good chance she still lives in town.