God makes His first announcement of Promise to Abraham in the following verse.
Gen: 12:2 Then I will make you into a great nation, and I will bless you, and I will make your name great, so that you will exemplify divine blessing. 12:3 I will bless those who bless you, but the one who treats you lightly I must curse, and all the families of the earth will bless one another by your name.”
During intervening period, Abraham doubts about this promise several times, as seen in these verses (Gen. 15:2,15:4-5, 15:8) and every time God reassures him.
Abraham believed God but his trust wavers every time when he ponders about his age. As God was continuously promising them (Abraham and Sarah) and with no off-springs of their own, they thought of taking things into their own hands instead of depending on God. Sarah did a foolish thing something which was against God’s wish.
Gen. 16:2 So Sarai said to Abram, “Since the Lord has prevented me from having children, have sexual relations with my servant. Perhaps I can have a family by her.” Abram did what Sarai told him.
Sarah tempted her men to try something against God’s wish. Similar instance we see with Eve. Sarah did not have patience to remain trusted in God and did something which she thought fit but it went against the wish of God. Ishmael was born because Abraham and Sarah did not trust God to fulfill His promise.
Gen. 16:16 Now Abram was 86 years old when Hagar gave birth to Ishmael.
And then the Sign of the Covenant.
Gen. 17:1 When Abram was 99 years old, the Lord appeared to him and said, “I am the sovereign God. Walk before me and be blameless. 17:2 Then I will confirm my covenant between me and you, and I will give you a multitude of descendants.”
There is no record in the Bible concerning the 13 years of Abraham’s life following the birth of Ishmael. But God’s rebuke shows that Abraham did not walk before God, and as a result, his life was full of blame. Also notice that God re-introduces himself as “God almighty.” God puts a condition to Abraham, saying walk before me blameless and only then He will confirm His covenant between Him and Abraham. Here God wants to reconfirm the same again with condition.
Change of names for a new begining:
Because of a lack of faith and doubt, Ishmael was born. This was not God’s plan for Abraham. God appeared and rebuked Abraham for not living before God and God’s promise. For 13 years there is no sign from God nor Abraham interacting with God. And that is reason for change of name of Abraham and Sarah:
Name-change signifies beginning of a new era and is all about redefining a person from what he was to what he would be. It is a reflection of a renewal that was to come in Abraham and emphasize his transition to be blameless. God wanted to rewrite a clean slate for Abraham from this point on and forget his past.