I know so much: Your first and last names are considered a collective
noun. But I don't know why that is.
First and last names together do not make a collective noun; they make a compound noun.
A noun is the name of a person, place, or thing. When a name, whether it is a person, building, or organization, or something else, points to a particular person, building, etc., it is called a proper noun. Some proper nouns are only one word: Mike, Albert, Snickers, Pepsi, etc. Sometimes two word or more words can be joined together to form a compound noun. There are rules for how they are joined together, which is another topic, but here are several compound nouns (remember they act together to make ONE noun): prizefighter, beach ball, newsstand, news room, sister-in-law.
When a compound noun is a proper noun, it too is still considered one noun, even if it spans multiple words.
John is in his office.
Mr. Smith is not in his office today.
John Smith is back in his office.
Mexico City is in Mexico. The Metropolitan Opera House is in New York. We have terrible news; the George Washington Elementary School has lost its credentials and will be closed down by the city.
Sometimes a person will go by an 'alias' which is like a fake name, a substitute name, used instead of the person's real name.
: otherwise known as --Webster's. alias. adv.
So, here you can use "are." My names are Wilbert Brown, Martin Thomas, and Andrew Welch. My real name is Wilbert Brown. Martin Thomas is my "pen" name I use in writing fiction novels, and Andrew Welch is a business name I use occasionally.
This is a real good explanation of how 'collective' nouns can be singular or plural: