The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same. ~Plutarch, Theseus
Finite creatures change, yet we are able to identify individuals in duration. What remains the same in the midst of growth or change? What constitutes the identity of any given object? More acutely, what makes any person himself, or herself, that person? This thorny philosophical question has attracted many attempts of solution.
For the Christian, the answer itself is simple, though unravelling the tightly woven knot of the truth is no less complicated than many of the answers offered by non-Christian philosophers. Despite the complications of philosophy, a simple apologetic can be briefly outlined:
1. God is the ground of all Being.
Paul, in his speech before the Athenian council, the Areopagus, claimed that the pagan poet Aratus' idea that "in Zeus we live and move and have our being" is rightly applied to the One True God who has expressed Himself in the man, Jesus Christ, who will judge the world in righteousness. To have one's being in God entails that one's identity is in some way derivative of God's productive activity, and insofar as God governs His productive activity, to that extent does He determine or maintain the identity of what He has made.
2. God is the fount of all knowledge.
The Psalmist, in comparing the wickedness of the wicked to the perfections of God, claims that God is the fountain of life and that in His Light we see light. While both "fountain" and "light" here are metaphors, the connotations are not so wide and various to obscure the likelihood that knowledge is in view. To see is to behold, to behold is to experience the truth of what appears, that is, to know it (at least to some extent). Combined with John's opening in his gospel, the metaphor is even clearer: Christ is the true light that gives light to every man entering the world. Darkness and blindness are opposing metaphors for ignorance, which also reinforce the meaning of "light" as knowledge. Thus, insofar as the identity of a thing, or of a person, depends upon knowledge, to that extent the identity of a thing is derivative of God's knowledge.
3. God is the end of all Being and Knowledge.
Not only is God the ground of being and the fount of knowledge, He is also the end of these things. Again John is our helper, for in Revelation he witnesses several times the declaration that Christ is the Alpha and Omega, the Beginning and the End. Nor is the phrase left indeterminate. In Revelation 21 Alpha and Omega is set in the context of Christ as the giver of life, which I think extends to the notion of Being quite directly, though I won't defend that assertion here. In 1 John 3:2, John tells us that the children of God are not yet fully known, but that they know that when they see Christ revealed they shall be like him. The Greek verb translated "see" is a metaphor for seeing with the mind, or knowing. Knowledge is transformative, but in a teleological fashion--we become what we are to be by beholding with the mind the completed revelation of Jesus Christ.
To put it narratively, we cannot know our full identity until the protagonist has completed the end of the story, for our identity as human beings are all bound up in his identity as the God-Man. This is certainly true, corporately, but also individually, just as every part of my body has a "story" of its own, the completion of which depends upon how my own volition directs it unto some final end.
To recap, the problem of identity within Christian thought finds resolution in the identity of God as the beginning and end of Being and Knowledge; by the decree of the Father made manifest to us (and all the cosmos) in the person of Jesus Christ, both Son of God and Son of Man, and declared true by the testimony of the Holy Spirit to all the members of His Body, the Church.