When God changed a person’s name and gave him a new name, it was usually to establish a new identity. God changed Abram’s name, meaning "high father," to “Abraham,” meaning "father of a multitude" (Genesis 17:5). At the same time, God changed Abraham’s wife’s name from “Sarai,” meaning “my princess,” to “Sarah,” meaning “mother of nations” (Genesis 17:15). This name change took place when God gave Abraham the covenant of circumcision. God also reaffirmed His promise to give Abraham a son, specifically through Sarah, and told him to name his son Isaac, meaning "laughter." Abraham had another son, Ishmael, through Sarah’s handmaiden, Hagar. But God’s promise to bless the nations through Abraham was to be fulfilled through Isaac’s line, from whom Jesus descended (Matthew 1:1–17; Luke 3:23–38). Isaac was the father of Jacob, who became "Israel." His twelve sons formed the twelve tribes of Israel—the Jews. The physical descendants of Abraham and Sarah formed many nations. In a spiritual sense, their descendants are even more numerous. Galatians 3:29 says that all who belong to Jesus Christ—Jew, Gentile, male, or female—are "Abraham’s offspring, heirs according to promise."
God changed Jacob’s name, which meant “supplanter,” to “Israel,” meaning “having power with God” (Genesis 32:28). This happened after Jacob had taken Esau’s birthright (Genesis 25) and stolen Esau’s blessing (Genesis 27), fled from his brother to his uncle Laban (Genesis 28), married Leah and Rachel (Genesis 29), fled from Laban (Genesis 31), and then wrestled with God as he prepared to meet Esau. Jacob had tricked his brother, been tricked by his uncle, tricked his uncle (Genesis 30), and was now going through his brother’s territory to escape his angry uncle. He’d heard that Esau was going to come out and meet him and feared for his life. That night, Jacob wrestled with a man, who later identified Himself as God and is considered a theophany or perhaps a pre-incarnate appearance of Christ. Jacob held on to the man until he obtained a blessing. It was at this point that God changed his name. No longer would Jacob be a supplanter and trickster. Rather, he would be identified as having "struggled with God and with humans and . . . overcome" (Genesis 32:28).
In the New Testament, Jesus changed Simon’s name, meaning “God has heard,” to “Peter,” meaning "rock" when He first called him as a disciple (John 1:42). It was Peter who declared that Jesus was "the Messiah, the Son of the living God" (Matthew 16:16). Jesus replied to him as "Simon son of Jonah," saying that he was blessed because God revealed Jesus’ identity as Messiah to him. He then referred to him as "Peter" and said that Peter’s declaration was the basis, or "rock," on which He would build His church (Matthew 16:17–18). Peter is also often seen as the leader of the apostles. Jesus occasionally called Peter “Simon” at other times. Why? Probably because Simon sometimes acted like his old self instead of the rock God called him to be. The same is true for Jacob. God continued to call him “Jacob” to remind him of his past and to remind him to depend on God’s strength.
Why did God choose new names for some people? The Bible doesn’t give us His reasons, but perhaps it was to let them know they were destined for a new mission in life. The new name was a way to reveal the divine plan and also to assure them that God’s plan would be fulfilled in them.