Can I add my full name after sir?

Yes, for the following reasons:

Mr is used before a person's surname, first name or position, as a title for a person without a title, or as a title for an official position, etc. It is used either with his first name or only with his last name, not only with his first name.

Like a guy named

John Smith, people can call him Mr. John Smith or Mr. Smith, but not Mr. John.

Extended data

Miss wrote the full text. It means miss (unmarried)

Madam is short for Mistreess.

Lady is actually the abbreviation of Miss and misunderstanding (whether you are married or not)

References:

Baidu Encyclopedia: Sir.