So yes, there can be 2 pets (as Jahan and Madora didn't back the game
)
Each party member can summon the same pet, including the companions so you can have four - and as Jacob notes, they hang around until killed.
It would seem better to allow only the first (player) character access to the Summon Pet skill, or have the skill just fail if a pet is present (and losing one in battle should result in a 5-10 minute delay before a new one can be summoned). But there's plenty of time for Larian to jiggle this in future updates (and hopefully, they'll open it up at some point so everyone can choose whatever pet they please).
