Princess Purryfinns is Linh Song's pet murcat. She purchased her in Book 6: Nightfall, from the shop Claws, Wings, Horns, and Things.
Marella states that she's "Pretty sure Linh did it so Tam would have to say the words ‘Princess Purryfins’ on a regular basis."
In Book 5: Lodestar, Grizel had proposed a game of Girls vs. Boys in finding Keefe’s "items of importance". Because the girls won, Tam bought Linh a pet.