It is true that when we present ourselves to others we are not only representing a company or a job but also ourselves and the important thing is to do our best.
That's what I try to do every time, to be myself, to be transparent and to make myself known as I am. But it has happened to me that in the past I have misrepresented myself, before I was very withdrawn, serious and often I could come across as unfriendly and little by little I have changed that. It has done me good and I represent myself much better.
Ii try not to get too personal in business situations, show too much of my personal self, however I am genuinely me all the time - a version appropriate for the situation - and *always show personality. It seems to get the results.
That's what matters and by being genuine those results come by themselves as a consequence. People notice those details.