Pet implies a level of tameness he doesn't have. He is one of the captain's creations, and evidence of why he doesn't usually make animals. They tend to turn out malicious like this. Just like when he makes plants, they're fucked up in one way or another.

Palamedes gave him the name.

[Not that it expects Alva to know who Palamedes is; Pal isn't even on the ship anymore, but. It's also an answer to the question of if he's a pet, in a sense. He was sufficiently loved to be named.]