Socrates, along with Plato, is one of the most prolific Western philosophers. Many critics agree that much of Socrates's life was told of through other philosophers. That said, one could use quotes attributed to Socrates to examine the question, "Who am I?"
The only true wisdom is knowing that you know nothing.
Here, one can assume that Socrates was open to the idea of not knowing everything, and he seemed to be okay with this idea. When looking at who one is under this idea, he recognizes that someone must accept that he or she really knows nothing in the grand scheme of things. The individual has limitations. To know one's self, one must accept these limitations.
To find yourself, think for yourself.
This quote is important in defining who one is because it forces them to question how he or she "fits" into the world. Socrates, here, answers who he is by making the decision to think independently, even if these thoughts differ from those en masse. One could answer the question of who he or she is by stating, "I am an individual who thinks for myself."
Let him who would move the world first move himself.
Here, this quote speaks to one knowing himself or herself because it recognizes the power of the individual. In order to change the world around one's self, he or she must first possess the strength to change himself or herself. Socrates's knowledge of the power an individual possesses to make change illustrates his own self-knowledge regarding his power to change the world. Only a person who knows himself or herself can openly and happily change.
This quote seems to be the most important in regards to answering the question of who one is. This quote leaves one's identity in his or her own hands, not relying on others. If one knows who he or she is, deeply, he or she can easily answer the question of "who am I?"
Therefore, Socrates not only answered the question of who he was in his philosophical studies, he helped mankind to answer the question for themselves.