Identity is a tricky business in Nazi Germany, especially if you are Jewish. To stay alive, a Jewish person must stay hidden. Being hated and persecuted takes a big toll on a person's identity, especially when it's combined with starvation, physical abuse, and the worst living conditions imaginable. For most of the characters, the situation makes guilt a huge part of their identities. A wrong move can result in instant death for loved ones, not to mention one's self. The novel's non-Jewish characters refuse to be identified as Nazis and forge new identities from friendship, love, and resistance to injustice.
Max's identity as the Jewish fist fighter helps him survive the Holocaust.
Until she meets Liesel, Ilsa Hermann's entire identity is built around the death of her son.