Pastor Chris discusses the story in the Bible where Jesus changes Simon's name to Peter, which signifies the role Peter will play in the establishment of the church. The speaker emphasizes that name changes in the Bible represent significant transformations in a person's life and that Jesus offers all people the opportunity to receive a new name in Him that reflects who they truly are as precious children of God. Pastor Chris encourages listeners to remain faithful and draw closer to Jesus to live more into their new name and become the person God has redeemed and called them to be.