“Game show with your name on it”

LORELAI: Mom, he’s not my type.
EMILY: Why not? Because I like him?
LORELAI: You know, I swear, I don’t know which one, but there is a game show out there with your name on it.

Lorelai is referring to the award-winning game show Jeopardy!, which was created by Merv Griffin and debuted in 1964; it is still in production. It is a quiz show where contestants are given general knowledge clues in the form of answers, while they have to offer the correct question to match it – very much like Lorelai and Emily’s responses to each other.