I'm not sure who the intended audience is for these texts, so I'll try to cover a range of interests and reading levels in this brief list:
The Outsiders: The conflict in the novel centers around the Socs, who are of a higher socioeconomic class, and the Greasers, who are of a lower socioeconomic class. The Greasers are known by their use of slang, and the narrator struggles with the label he's been given despite his ability to do well in school, which most Greasers aren't able to do.
Where the Crawdads Sing: Kya grows up completely alone, deserted by her entire family, and becomes known by the identity of "Marsh Girl" by her town who ostracizes her. She learns to find her confidence in this identity and becomes a successful scientist by becoming an expert in marsh creatures.
Divergent: Tris struggles with aligning herself with the identity of her family or following her heart. She learns that she is Divergent and cannot belong to any singular faction.
To Kill a Mockingbird: Themes of identity, language, and culture run throughout the text. Scout notes that Calpurnia speaks one way in their home and another way with her African American friends at church. Scout learns of the racist culture of Maycomb through Tom Robinson's trial. She forges an identity that is less childlike as the plot progresses; for instance, she goes from viewing Boo Radley as an object of fascination early in the novel to realizing his very human struggles and strengths as the novel closes.
Lord of the Flies: After being isolated on an island, the majority of the boys begin to lose their civilized and rule-abiding identities in order to follow Jack, who represents anarchy. As they shed their former identities, their physical identities also change, as they look increasingly savage as time passes. Their language also degenerates into a more savage, uneducated speech as time passes.
Narrative of the Life of Frederick Douglass: Frederick Douglass notes that when his book was published, people didn't think he could have possibly written it because he was a former slave, and slaves weren't thought capable of such complex rhetoric. Douglass also explains how learning how to effectively master language opened his mind to an entirely new world of thought.
The Great Gatsby: Gatsby has created an entirely new identity for himself in order to attempt to win the love of Daisy.
The Bell Jar: Esther dreams of becoming a poet and lands an internship in New York. However, once there she struggles with her identity and the general expectations of society.
Uglies: In a dystopian setting, Tally lives in a society where everyone receives a surgery at age sixteen to make them perfectly "pretty" in every way. She finds herself battling this thinking and finds her own identity along the way.
I hope this is enough to help you and/or help you think of other texts that might work for your particular audience and goal. Good luck, and happy reading!