Before that, Abram and Sarai seek to outwit God by making a deal with Sarai's maid, Hagar, to bring an heir into the world. God called them to task for it. It is promise. It is announcement. Often in Baptism another name is given to a child - a baptismal name.
Promise lies in such words, in that kind of naming.
Prior to Abram's name change, Abram primarily listened, struggled to obey, schemed and complained. Following the change of name, you see a change in Abraham, who calls God to account on behalf of Sodom and Gomorrah. Abraham argues that God ought to be more considerate than what God was contemplating. Abraham bargains with God, pleads with God, argues against God's intent. This is not the Abram of Ur, or the early days in the wilderness that would become Israel.