Here's why it's not a common or proper noun:
* Common nouns are general names for people, places, or things (e.g., dog, city, book). "His" doesn't name anything.
* Proper nouns are specific names for people, places, or things (e.g., Fido, London, Harry Potter). "His" doesn't refer to a specific person or thing.
Examples:
* His dog is friendly. ("His" shows that the dog belongs to someone.)
* His name is John. ("His" shows that the name belongs to someone.)