Is it capitalization that forms a proper noun?

No, capitalization is not what forms a proper noun. There are some proper nouns that do not use capital letters (m&m's for example) and far too many people that capitalize incorrectly. A capital letter does not make it a proper noun.

What determines that a noun is a proper noun is what the Word is for. A proper noun is the name of a specific person, place, or thing. The noun "m&m's" is the name of a specific candy and a registered trademark, a proper noun.

Common nouns are general Words for people, places, and things.

Proper nouns are the names of specific people, places, and things.

The noun 'doctor' is a common noun; the noun Doctor Jonas Salk is a proper noun, the name of a specific person.

The noun 'city' is a common noun; the noun New York City is a proper noun, the name of a specific place.

The noun 'bridge' is a common noun; the noun Brooklyn Bridge is a proper noun, the name of a specific thing.