Let's imagine a situation where I know two persons with the same name... Kevin for example... The one is my friend, and the other works at Coca Cola... Will I say: My Kevin, not the Coca Cola Kevin. OR My Kevin, not Coca Cola Kevin.
The expression "Coca Cola Kevin" is casual English.
You would only use "my Kevin" and "Coca Cola Kevin" in a context where your listeners know who you are talking about.
You could happily use either form (with or without "the").