What are proper nouns of people's names called?

Question

Proper nouns include any named entities, often appearing in title case. These include places and other entities such as organisations and groups. What is the concept of a person's name called?

Answer 1

They are called anthroponyms.

Answer 2

Wikipedia is worth quoting here.

A proper noun or proper name is a noun representing a unique entity (such as London, Jupiter, John Hunter, or Toyota), as distinguished from a common noun, which represents a class of entities (or non-unique instance[s] of that class)—for example, city, planet, person or corporation. In English, proper nouns are not normally preceded by an article or other limiting modifier (such as any or some), and are used to denote a particular person, place, or object without regard to any descriptive meaning the word or phrase may have (for example, a town called "Newtown" may be, but does not necessarily have to be, a new [recently built] town).

Thus "Andrew" indicates a named entity and is a proper noun.

Names are always proper nouns, even when you are artificially using them as common nouns in expressions like "some Andrews", "any London" (there is a London in Ontario and the UK).