An individual's identity is impacted when they experience oppression. In Persepolis: The Story of a Childhood, the outcome of that oppression on an individual appears to be determined by where that oppression comes from.
Marji experiences oppression during the cultural revolution in Iran from the people outside her family. She's forced into a different style of living but still retains the love and support of the people closest to her. This makes her stronger because oppression isn't all she knows. It helps her fight back against the oppression that she sees. For example, she tells her religion teacher off at school when she is 14. This is what leads to her parents sending her to Austria.
Her grandmother tells her, "In life, you'll meet a lot of jerks. If they hurt you, tell yourself it's because they're stupid. That will help you keep from reacting to their cruelty. Because there is nothing worse than bitterness and vengeance. Always keep your dignity and be true to yourself." Lessons like this help keep the oppression she experiences from twisting Marji. They help her be strong and caring.
However, oppression from anywhere can cause anxiety and depression. When she loses her uncle, she feels "lost without any bearings." When the bombings start, she has to be constantly on edge, waiting for the next danger. She has to worry about being reported for a wide variety of things. These have an impact on her identity because they make her a more anxious and less trusting person.