Interesting thought. Kind of makes you realize how multi-faceted existence is when you try to step outside yourself.
No, I don't know "me" all that well. The parts of me I know well are the bits related to my own behavior patterns, habits, likes and dislikes; the predictable me. Not terribly interesting, or unique I'm finding. I guess I'm like tree, I'm not much surprised by me, either.
The self talk that goes on almost constantly is telling me a variety of "perceptions" of me, sometimes I think that voice is that of other people with whom I associate, other times I recognize it as my own perception of myself which is usually influenced by how I'm feeling at the time. Did I have a really good run on a new trail? Man, I'm awesome! Did I forget to do something I said I'd do? I'm worthless. Either way, it may be accurate at the moment, but it is not my true self. Not an illusion, but elusive and mutable.
And the sense of me gained by all the introspection I engage in? Much of it is forgotten unless I write it down or it becomes a sort of slogan at worst, a mantra at best, to be replayed on a loop while I am engaged in some activity. That which gets written down is often looked upon with amusement at some later time. Did I really think that? Some of it has kernels of truth and wisdom, though.
But would the perceptions of others help me get to know me better? I don't know, maybe a little bit. It would depend on what their motive is, and I'm not sure I'd trust that. I normally take such observations, I guess I'm talking about feedback, as useful bits of guidance, encouragement, or criticism. But I think I place that in the same place as my own self-talk, maybe accurate at the moment, but no measure of a true me.