It's not my assumption, it's Seven's own words:
COMPUTER: Identify self.
SEVEN: Simply check my voice pattern. You'll find me listed as Supervisor one nine four. Code name Gary Seven.
You can take up the definition of "code name" with him if you like, but he called it a code name, and that means it's not his real name -- which is the point.
So, to get back to what I was assuming about Gary Seven, I was assuming that the code name Gary Seven was assigned to him at birth, to ensure that he has a unique name for all time in the organization. Heck, maybe he didn't even know or use that code name growing up. Maybe only once he graduated into training to become an agent was his code name revealed to him. He could have been given a name by his parents that was entirely different, I'll acknowledge that.
Then why are you arguing with me at such length????
If we're agreed that it wasn't his real given name, that's the end of it.