If you ask people 'Do you know who I am?', it means that you are somebody – someone with some fame or power or authority and probably you are in the news regularly so you expect people to know who you are.
Normally we say ' Do you know me' not 'Do you know who I am'.
For example:
“Do you know me? Why do you keep looking at me?”
“Do you know me? I stay in this block too.”
