She did not want to be known only as the wife of her husband. She insisted on having her own 'identity'. [=on being known for her own qualities, achievements, etc.]
The face of the witness was hidden in order to protect her 'identity'. [=to keep her name from being known]
He has a strong sense of personal 'identity'. [=a strong feeling about exactly the kind of person he is]
(..) I work because I love my job. Understood. But you can't love it as Ana Grey? I need to have my own identity here. People already think I got to where I am because of you. But you didn't. You got this through hard work and talent. (..)2018 Fifty Shades Freed