In the episode “A Deep Fried Korean Thanksgiving.”
LORELAI: The cat’s name is Kirk?
KIRK: Yup.
LORELAI: Weird coincidence or…
KIRK: I named him Kirk.
LORELAI: Isn’t that confusing?
KIRK: Not when you think about it.
LORELAI: No, it’s still confusing.
KIRK: I like the name, and whenever I call Kirk’s name, I obviously won’t be calling myself… Although when my mom calls for Kirk, that may be confusing. Maybe I can get her to say Cat-Kirk when she’s calling Kirk, and Human-Kirk when she’s calling me.
RORY: That would keep it straight.
KIRK: I’m glad I ran into you. See ya.
LORELAI: See ya, Human-Kirk!
RORY: Bye, Human-Kirk!
Around Thanksgiving, Kirk purchases a cat from an unspecified “lady at the super market.” (Rory explains to Lorelai that he’s always been a cat person, but never had cats.) Kirk then tells Rory and Lorelai that his cat is named “Kirk.” Lorelai asks if it is a weird coincidence, but Kirk assures them it’s not: Kirk named his cat “Kirk.” Lorelai asks if such a thing would be confusing, having the same name as you cat. Kirk originally says no but then thinks otherwise. He concludes that when his mother calls one of them, she can say “Cat-Kirk” or “Human-Kirk” so they won’t get confused. Lorelai walks away with Rory, quipping, “Bye Human-Kirk!” This becomes a running joke throughout the episode.