Who am I?

We frequently use "I". But how often have me thought who is this "I"?
Your name? (Mine is Kelvin) But there are hundreds, if not thousands or millions of people with the same name.

Our physical manifestation? What if i accidentally (touches wood) sliced myself into equal parts of two? Would it be like how amoeba splits into two separate entity? Which one would i be then? Or would i be like a pair of twins? But even twins have a separate thought system.

Ok, maybe that was a bit far-fetched, but I hope you see my point.

So what is you take on being? Who are you? What constitutes you?