Identity is an interesting thing. Jordan Peterson makes the observation that it is indeed a public thing, but like reputation it is publicly constructed more than individually asserted.
Our current POTUS surely has an opinion as to what his reputation should be. He would love to use the rule of law to make the nation mirror his beliefs about himself. He can love that all he wants. The minute he tries to make the nation do so by using the law he not only violates the first amendment but he also refuses to understand reality. His reputation will be fractured in as many persons there are and in as many moments as those persons consider his person.
Identity is kind of like that. We might like to assert it independently of any other constituent reality but that assertion will always fall short.
Christians believe that our identity comes from God. Christians believe that however God identifies us is the identity that will finally and ultimately endure because, as with the reputation of people, all imagined identities are subject to the imaginers and if there is truly only one final imaginer, who was also the first imaginer, then this imaginer will finally be the one whose imagination prevails.
We not only live before an audience of one but we exist by that imaginer/audience as well. We are contingent beings and will always be dependent upon the non-contingent one to be.