"To have an identity" means to have a sense of who you are as a person. It includes your characteristics, beliefs, values, and the way you see yourself. Full definition
And if it's still having an identity crisis in its past, then what about the party's future? (totalpolitics.com)
That's why we've developed a system that allows you to search for sex without having to worry about having your identity discovered. (sexsearchcom.com)
But they just don't have the identity of a lot of the other teams. (justarsenal.com)