Great question! There is actually a great deal of renaming in the Bible and only some of it is from God. Some people renamed themselves. For example, in the book of Ruth, Naomi chose to be known as “Mara” because of the bitterness of her grief. Other times, one human would rename another, as in the case of Daniel and his 3 friends in Babylon.
A person would rename themselves, or rename another to either symbolize an event or experience (Naomi, for example) or to make them more culturally appropriate (Joseph in Egypt, Daniel in Babylon for example.)
But, to the question, here is a quick list of people God renamed in Scripture:
Abram and Sarai became Abraham and Sarah
Jacob became Israel, (The deceiver becomes the one who contends with God.)
God changed Pashhur’s name after he physically attacked Jeremiah the prophet. God renamed him “Terror on Every Side.” Jeremiah showed some incredible courage, delivering that news to Pashhur after receiving his beating. Meanwhile, I think we can all agree that the second ‘h’ in his name is redundant or silent.
Simon “the Reed” became Peter “The Rock.”
James and John became “The Sons of Thunder!” (But hey, that may have just been Jesus’ nickname for those hotheads.)
One of the more tender renaming projects is when God first named Hosea’s children, born to an unfaithful woman. God had Hosea name them, “Not My People” and “Not My Loved One.” (Its a bit snappier in the original Hebrew.) Later on, God renamed them, “My People” and “My Loved One” as a powerful metaphor for God’s forgiveness and mercy. I would encourage you to read this for yourself, its a stunning move right there in the Old Testament.
Some think that God changed Saul’s name to Paul, but actually, he always had those two names. Paul/Saul was Jewish, but a Roman citizen. “Saul” was his Hebrew name and “Paul” was his Latin equivalent that made sense in the Roman Empire. In much the same way, I like to make people call me “Esteban” whenever I’m south of the border. It makes me appear more exotic and I can use all the help I can get.
So, in brief, God changes a name (or in many other cases, assumes the naming right of a child) to make a point. It usually coincides with an event, or a prophecy and we should consider each renaming or naming of a baby on its own merit to best understand why God did it.
So, for example, the renaming of Simon to Peter. Simon means “reed” and Simon was often easily swayed by the winds of the day. But after he made the confession that Jesus is the Christ, the son of the Living God, Jesus renamed him “Peter” meaning “Rock” which, of course, is not easily swayed, but is steadfast. Jesus was both marking the moment of that confession and also speaking into Peter his future reality. As we read the book of Acts, we see this previous reedy guy standing steadfast in the face of the strongest opposition, continuing to proclaim “Jesus is the Christ, the son of the living God.”