When Abram entered into a covenant with the Lord, he was given a new name – Abraham. This represented a new beginning, symbolic of being born again. (Gen 17:1-8) Likewise, Sarai was given the new name of Sarah. (Gen 17:15-16)
When Jacob entered in a covenant with God, he was given a new name – Israel. This was symbolic of being born again, and represented a new beginning. (Gen 32)
When Simon became Peter and Saul became Paul, their new name represented a new beginning, symbolic of being born again. (John 1:42; Matt. 16:16-18; Acts 9:1-19; 16:37; 22:25-28)
Jewish infants are circumcised on the 8th day in honor of the Abrahamic Covenant. At that time, they are given a new name, and a new beginning. (Gen 17:9-14)
When we enter into the covenant of baptism, we are born again. As with our mortal birth, we take upon us the new name of Christ, our spiritual Father. This is a new name and a new beginning.
Each time we renew our covenants of baptism by partaking of the sacrament, we once again take upon us the name of Christ. This is a new name, and a new beginning. This is also symbolic of being born again.
When we enter into the temple covenants, we are born again and given a new name. This is another new beginning. (D&C 130:11-12)
This is a glorious pattern.
Heavenly Father is a God of second chances and new beginnings.