In Othello, Shakespeare explores factors that play an important role in the formations of one's identity – race, gender, social status, family relationships, military service, etc. Othello is also concerned with how an individual's sense of identity (which can break down and be manipulated by others) shapes his or her actions.
Othello's rage at Desdemona's infidelity has nothing to do with his love for her; rather, for him, it signals the destruction of his own identity as a successful and loved man.
In Othello, a man's reputation seems to hinge on military duty and public behavior, while a woman's identity often hinges on her sexual reputation.
Iago's true identity is ultimately unknowable – for the play's characters as well as the audience.