Names are powerful things. They are the core of our identity, so much so that we may insist on being called by one of our names (first or middle) to the exclusion of the other. Tolkein understood this; in the Two Towers, Treebeard cautions the hobbits not be hasty lest they give out their real names. Names, according to Treebeard, tell the story of those they belong to.
Names also give us control over someone. If you have some one's name, you can Google it and perhaps find out more about that person than they want you to. In Jurassic Park, the main character marvels at children in museums who master the complex names of dinosaurs that their parents are unable to pronounce, as if by saying the name, they have gained a measure of control over the terrible beasts.
It might seem strange that something which we are given can have such power; but once given, it defines us for all our days. There is little wonder though, if you look at the Bible. All the names in the Bible have a specific meaning; Moses is similar to the Hebrew for "draw out," as he was drawn out of the water. Jesus is a translation of Joshua, which means, "the Lord saves." The Bible clearly illustrates the importance of name to a person's identity. The Third Commandment even forbids profaning the name of God.
Perhaps the best example from the Bible comes from three people whose names changed: Abraham, Jacob, and Paul. All were chosen by God, and none were what you would call saintly material in the beginning. Abraham was a nobody, Jacob was a conniver, and Paul persecuted and murdered early Christians. But God chose them not for their qualities, but to illustrate his power to take something bad and put it to use for good. He does this with every Biblical hero, but these three are special in that their identity changes completely, evidenced by their names.
Abram was chosen by God to be the foundation for His chosen people. He became Abraham, "father of many." Jacob, "the supplanter," stole his older brother's inheritance. He became Israel, because he "struggled with God and with men and [overcame]" [Gen. 32:28] Saul, the Pharisee, the strict religious Jew, became Paul (from Paulus, a Roman name), was "humbled" and became the Apostle to the Gentiles. Once they belonged to God, these men were not the same as they were before; they were new persons.
God can change your identity as well; by letting him come into your life, by accepting His gift of salvation through Jesus Christ you become a new person, as surely as if you changed your name.