Personally I think the Dog should behave more like fellow campanions/party members, like the Blacksmoth's dog, he should have attacks the the player can pick from.
That gives us the option to do attacks, skills & block.
Attacks & Skills:
-Bite= does small DMG
-Grapple= Stun or restricts Agility
-Bark= makes enemy miss there next attack
For example
I think at the beginning it should be more contingent on what he is attacking... for example attacking a Humanoid, it makes most sense for him to lock onto an arm or a leg (Immobilizing or Tripping the target), unless the target is prone, (in which case the throat becomes a much easier target), if it is a quadruped like a Wolf or a Bear, going for the throat or belly/groin makes more sense (potential for both nonlethal (submission grip on neck) & Lethal, (tearing out the belly/intestine/genitals).
Ideally IMO there would be a training Dynamic that would allow the player to pick/enhance Dogs attacks rather than it being situational/random, maybe a feature of the guy who sells the dogs, pay for obedience courses.
I'm not a fan of a "Bark" attack in combat (Bites tend to be better than barks regardless to the popular saying

), but I can see the merit as an intimidation tactic if there were ever "charisma" checks in various interactions (and Barks would be a cool feature to warn of ambush or flush out prey).