What you do' is your profession and is certainly a part of who you are, but it's not the whole story of you. The 'what you do' does not define the 'why you do it' and if you can explain the 'why you do it' then you can better answer the question 'who are you?'.
At it's core, the 'who you are' is your purpose or raison d'etre (reason for existence) and so adds your passion, your mission and your vocation to your profession. These components that define your purpose are created by the overlapping attributes of what you love, what your world needs, what you are paid for and what you are great at.
This graphic puts it all together so beautifully ...