Christian>>> In the context of introducing yourself you should use the singular form. “My name is John Michael Smith.”

Even if your full name consists of more than one first name as in your example (“John Michael ”) it’s still treated as a singular object. The difference between the singular and plural version depends on the context. For introduction, there is no need to emphasize the number of first names since this would force an interpretation that you go by different names in different situations or that you have different identities, etc.
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...Sometimes a person will go by an 'alias' which is like a fake name, or a substitute name, used instead of the person's real name. 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. If I said "My names are " Onuoha Uchechukwu Christian Omodara" it would sound as if I had two or more identities