When we touch an animal it is "pet" or "pat"?
Should we say "Can I pet" or "Can I pat him" (a dog)?
When one approaches a stranger's animal, it is polite (and wise) to ask,
May I pet your dog? or, May I pet him? If you do not know the animal's gender, it might be preferable to say your dog to it, although it is perfectly grammatical. One might do this as a way of respecting strong feelings one may have for a pet.
As for "pet" or "pat", both are correct. Pat connotes a light, quick stroke with the hand.
She gave him a friendly pat on the arm.
To pet an animal is to stroke or caress gently; pat; to touch or stroke in an affectionate or loving manner.
When I pet my cat, I feel very calm.