* If you're referring to the name "Harry" as a proper noun, then no, you don't italicize it. Proper nouns are names of specific people, places, or things, and they are generally not italicized.
* If you're referring to the name "Harry" as part of a title, like a book or movie title, then yes, you would italicize it. For example: *Harry Potter and the Sorcerer's Stone*.
Let me know if you can provide more context, and I can give you a more precise answer.