God further said to Abraham: "As for your wife Sarai, do not call her Sarai; her name shall be Sarah. I will bless her, and I will give you a son by her. Him also will I bless; he shall give rise to nations, and rulers of peoples shall issue from him."
I find significance in God's instruction to Abraham, "Her name shall be Sarah!"
A name is a relationship. Somewhere in this endless blog I have offered that thesis. If a human being could live alone in the wilderness out of contact with all other people she would need no name. There would be no one to call her by name.
When Adam named the creatures he appointed their significance to human beings. Notice he was given the privilege of naming the woman God had given to him: "The man gave his wife the name “Eve,” because she was the mother of all the living."
When God names her Sarah God claims a relationship with the wife of Abraham that the patriarch must respect. Though he may certainly use the name, it wasn't his name for her, nor was she his personal property.
Sarah's independence would become pretty clear once Isaac was born. Although she had appointed Hagar to bear Abraham's only heir, albeit an illegitimate one; once Isaac was born Hagar and the bastard had to leave. Sarah would not abide them in the camp with her son and her husband. Abraham might feel pity for the slave and her child but he had to obey his wife.
Several thousand years later we still struggle to stabilize and normalize the relationship of husband and wife, men and women. One approach is to deny there is any difference between men and women. Both can be lawyers, doctors and teachers; both can be soldiers, boxers and priests. Can both be mother and father? I know one woman who appeared to be "the husband of her wife" until she also had a baby. (I didn't ask how that happened.)
To make sense of it all, Abraham took his cue from God. There's some wisdom there.