The groups you share a common identity with are called what?

Depends what kind of identity you share. They may be your racial group (shared physical appearance, usually), your ethnic group (shared cultural background and religion, usually), or people of your nationality (from the same country as you). In Psychology, people of your same approximate age and cultural situation are called your "cohort," and people who are in your same educational or professional group are called your "peers." I hope one of these is what you're looking for!