Abram means highly honored father, exalted father. Abraham means father of many nations. Undoubtedly the name has to do with God’s purpose, His promises, the role that he was going to be playing in the purpose God was working out. So God gave the name change as both a sign and a seal to Abraham for his altering role in the purpose that God is working out.
It takes two to tango. If Abraham was going to be the father, Sarah was going to be the mother. She is very important to us as well. Sarai means female noble, or queen. Sarah means essentially the same thing.
Adam Clarke in his commentary makes an interesting suggestion that Sarai seems to indicate position in family and Sarah within or over nations. Sarai describes a position in relation to Abram and Sarah describes her role as Abraham’s wife, the wife of the father of many nations.
There are some disagreements over what Sarai means. Sarai means female noble, that is the one that is most consistent with those who do research into this kind of thing. There was one though, a man named Elson Smith. He felt that Sarai indicates someone who is contentious and quarrelsome. Nobody seems to doubt that of the names come from the same root, Sar, and it is the feminine of the masculine word that we would translate “captain or commander.” In Isaiah 49:23, Isaiah used this word and it is there translated in the English Bibles, “queen,” Sar is translated queen. The root idea gives one the impression of ruling, as a captain would over a group of men, or as a queen would. It indicates ruling.
This is undoubtedly why Adam Clarke feels that Sarah’s name was changed in order to indicate position and relation to Abraham. Just as his name was changed to indicate his role in God’s purpose, so her name was changed to indicate her changing role within God’s purpose as well. As Abraham was to be father of many nations and be a ruler in that sense as a patriarch over them, so Sarah is to be a matriarch, and she also a queen bearing rule over nations. Notice what it says in verse 16.
To me that indicates the name change indicates that the covenant was made with both Abraham and Sarah. We tend to think of it only in relation to Abraham, but I think the name change indicates, to me any way, very clearly with Sarah as well. It is not something just for a male. You will find reference to something like this in Galatians 3, for example, where it says,
Years have passed since Genesis 12, Abram already has a son but that is it, that son is not the one that God promised him. So he does not really have a descendant yet, but here is God promising as many descendants as all of those stars that he can see and not see up there. After this sequence of events they entered into a covenant, and the circumcision was begun.
Now there you have it, there is the promise that produces the body of people who, in Romans 9, are in a physical sense within the mass of Israelites, and even as Ishmael, Abraham's son, engendered by natural means, was physically with Abraham's family.
Paul's point in referring to the "promise" is that Isaac's birth was wholly God's work. Get that, it was wholly God's work. Sarah could not bear a child, and the child produced by Abraham through Hagar was disqualified as not being the "child of promise." God was showing that any child produced in the way that Abraham produced Ishmael was not going to be the "child of promise." This is why Paul, in Romans 9, calls these people as being named after Isaac the "children of promise."
So what Paul is talking about in Romans 9 is a separated group, a family named by God after Isaac was born to Abraham and Sarah one year after God made the promise. Therefore, some individuals who begin life as part of the mass of Israelites are separated by God to be part of something else that is also called Israel. Thus we begin to perceive the beginning of a Biblical truth regarding how God sees us in this picture.
To pick things up here a little bit and speed on, Abraham sired a child. This man whom God picked, who doubted Him somewhat, went on to even offer his son, Isaac, which means "laughter" because God reminded him of his lack of faith. This man, caused to be the father of the faithful, continually grew to where he could even offer his son before God. This man started out in a weak condition. God had faith in Abraham. His faith was justified and the choice that God made was correct.