"It's the cat that writes that online thing."
"The [library's] cat is really cute."
"What does that mean?" (pointing to my name)
"Look, it's Cauli" (pronounced as Cay-Lee) (but see corrective note below).
"Is that the cat at your library?"
Corrective note: It's pronounced Call-Lee, like the vegetable cauliflower. But Cay-Lee has a nice ring to it, too.