I used "that someone is me" which feels natural to me and expresses exactly the same concept. It was not accepted.
That would be "Én vagyok az."
But it is a good guess. I would say:
"I am that somebody."
My problem with this sentence is, that AZ/THAT is not possible with ME. It should be EZ/THIS to be logic. And EZ a valaki èn vagyok could be maybe translated with: This (one/somebody) is me.
Perhaps you are looking at a picture on a wall and somebody says, "Look, there is Sylvester Stallone coming out of a nightclub with someone" and you say, "That someone is me!"
Since the picture is not close to you, it's "that picture" rather than "this picture" and I think it would also make sense to say "that someone" rather than "this someone".
OK, I got it. :-) I had the imagination, that somebody says this to another person on the street, showing to himself at another place. LOL (that somebody)
"I am that somebody" wasn't accepted, so I have reported it, as I think it is correct.