Names are important in the bible. Remember how Adam named the animals? I explained that it was an act of dominion or power. It is similar here; God is expressing his lordship over Abraham. It's interesting because his new name (Father of a multitude) has a very similar meaning to his old name (exalted father). Both of the names emphasize his descendants, which must have been particularly grating through his many years of childlessness, but also emphasizing the contrast of God's promise and his inevitable children.
So God renames Abraham. This serves to reaffirm God's promise, having many descendants, it serves to affirm God's sovereignty in his life, and it also establishes Abraham in a new season in his life, forming a discontinuity with the old life (and the old name). Abraham enters the covenant of circumcision and God promises the birth of a son through his wife Sarai.
On that note, God renames Sarai as well, to Sarah. This has the same meaning and impact as Abraham's new name. Both Sarai and Sarah mean "princess", so rather than establishing a new direction for her life, it reaffirms God's existing promises and sovereignty in her life. However, God does specify now that Abraham's promised son will be born from Sarah. This has important results. First, it is a strong validation of Sarah. Not only is the promise a son for Abraham, it's also a promised son for Sarah, and given everything I said about the importance of women bearing children in this culture, that must mean a lot to her. God is only speaking to Abraham here though, so we will see her reaction later.
Second, in spite of God saying he will bless Ishmael, it raises some important questions about Ishmael's status. Since Isaac is the child of the covenant, what does that make Ishmael? One can easily imagine that Abraham and Sarah spent the last 13 years thinking that Ishmael was the promised son. Certainly their incredulity at God's renewed promises implies they were not expecting another child to come. And in spite of how Abraham values Sarah over Hagar, it just had to be difficult on Sarah to know (or think she knew) that she would never have a child. But now that we know there will be another son, that Ishmael is not the promised son, one can only imagine that this relegates Ishmael to a sort of second class in Abraham's family. We will see the outcome of this later.
Third, it casts further doubts on Abraham's decision to sleep with Hagar. Of course, as I pointed out this is the first (recorded) time God says the promised son will be born through Sarah, so one could defend Abraham's ignorance here, but regardless of his knowledge or motives at the time, it is now pretty clear in my opinion that trying to have a son through Hagar was a mistake. And I think Abraham is probably beginning to think similarly. Yet even without the covenant and the promise, Ishmael is still guaranteed blessings and to be a great nation. So the blessing of Abraham overflows to his children, even those who are not the promised of God.