Perhaps it depends if you have dogs or not. I have three dogs and they are definitely WHO.
But I agree with SuKi (she's usually right so I have to agree!) that Which dog is Coco? would be the more usual way of putting it (if there is a group).
In general, Who is Coco? is fine to use as a question, especially if you just hear the name 'Coco. "Who is Coco?" "Coco's a dog." "Oh, Coco's a dog."