I'll go with two of my favourites, and some recent discoveries:

One book that has had a profound impact on my worldview at the time is Stiller, which, as a novel, explores how identities are not only constructed by ourselves, but also those around us.

I have also enjoyed many books by Milan Kundera, who might be known to many of you. Identity was a particularly interesting one to me, besides his probably most famous one, The Unbearable Lightness of Being. His novels explore many topics ranging from love relationships, philosophy, and the political context of the Cold War, through the lens of the situation in the Czech republic.

Finally, Waiting for Bojangles is a recent novel, very original and touching take on the fine line between eccentricity, and mental illness (with very inventive language!). No idea though, how well the translation into English went.

On a the non-fiction side, Eva Illouz has interesting takes on emotionality in times of capitalism, and the influence of psychology/psychotherapy on the modern self.