I think essentially you and @
William agree, he just points out that in order for your self image to be more than just daydreaming you need interaction with the world to actualise it. Like his example; I could lay in bed daydreaming of being a masterful lover, and in a sense that could be my reality, or identity, until I die, but unless I go out to other people's beds and make love to them and achieve mastery and the ensuing social recognition it won't be more than just day dreaming.
ofc this leads to a discussion of epistemology, is actualised identity better than imagined identity? There is no hard reason to think so, but to be honest people who actualise their identity always seem more real to me than those who don't. But that's personal taste maybe.
edit: Sartre had the idea that identity only takes hold when you die, because up to then there is nothing that you fall together with, that is, you're in change, are you a salesmen? What if you get fired? Are you sle? What if you get brain damage and start performing the world as ese? Are you a good person? What if you get in a war and have to do terrible things or make a terrible mistake?
after you're dead you've been fully actualised, you are what you were.
i think, together with his "hell are the others" statement sums up my ideas about identity nicely.