I think one can have an identity as a writer as long as one writes, talent or lack thereof would not stop one from being able to consider it as an identity. I think one can identify oneself as a kind person if one believes one is being kind - people can interpret kindness differently (just look at the varying responses on this board to descriptions of the range of what one person considers kind, another will find cold and still another hostile and so forth)
I would put character more in line with a manifestation of personality - moral underpinnings.