Then God said to Abraham, “As for Sarai your wife, you shall not call her name Sarai, but Sarah shall be her name. And I will bless her and also give you a son by her; then I will bless her, and she shall be a mother of nations; kings of peoples shall be from her.” (Gen 17,15-16)
So Sara will also get a new status, as evidenced by the change of her name. In those days, newborn children were not yet registered in the registry office, there was no set of recognized names, no calendar, and no holidays... so people could make up their children's names at will. That's why names were more meaningful, parents put their wishes, expectations, characteristics into them. Many times we see in the Bible how a child's name was clearly prophetic in nature. Indeed, in many cases God Himself (as now with Isaac) told the parents what name to give to the child. If the name bore a special meaning, then it certainly had an effect on the person. Exotic names are now given to children more often than in earlier decades, but nowadays it is more for the sake of lilt. However, some time ago, a research was carried out which came to an interesting conclusion: children with exotic names were statistically more successful in their studies or careers in some respects. The conclusion was that their special name gave them the impression of a certain exclusivity, of support from their parents, of an expectation of a special destiny. This helped them in their confidence that they could achieve it.
But in God's kingdom it is not about what we achieve or about statistics. But the name does have an impact here, "And I tell you that you are Peter; and on this rock I will build my church, and the gates of hell shall not prevail against it." (Matt. 16:18) We know the actual wording of the original text and its pun - the change of Peter's name is from the Greek "Petros" (stone fragment) to "Petra" (rock). Jesus changed Peter's name after he received a most important revelation from above. Yes, God has a tendency - beginning with Abraham - to change people's names when something spiritually significant happens in their lives - or when they achieve a different status. Peter was just then blessed and given a new name - it is not only in the Old Testament, Jesus does this in New Testament times too!
But notice that God did not completely change Abram's, Sarah's, or Peter's names, He only modified them. God is not only the best linguist (after all, the word came from Him, it was already there before creation...) But it is also a beautiful picture of God taking hold of man as he is, not quite erasing his personality, but transforming it into His image - crowning it with heavenly things.