"who I am" and "what I do" suggest permanent character traits, habitual ways of behaving. This is what the writer wanted to express. Consider that "what I did" would refer to a specific action in the past, but "what I do" suggests "what I always do", "what it is in my nature to do".
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lukandSomeone said: 'My name is John'. After some time somebody else reports this event: 'He said his name was John'.Changing to "was" is called backshifting. There are two facts about backshifting that must be kept in mind.