The Lord comes looking for the man and woman, and the nature of the questions God asks and God’s response to the serpent make clear that the man and woman belong to God, not to the serpent (“enmity” is the clarifying term here).
The Lord promises that the woman’s seed will crush the serpent’s head. Adam and Eve had assumed death was the consequence and the end of the story. Instead, a “future history” is promised. A “grand narrative” is coming, of which they are the first chapter, and all who follow will fill the subsequent chapters until the serpent’s head is fully and finally crushed forever. We are part of that narrative, and are called to know it and our place within it.
This future history is filled with surprising and unexpected hope: the “mother promise” of all biblical promises.
The rest of the chapter strengthens this hope by reaffirming our calling and by providing our equipping:
the mandate of Genesis 1 to multiply and fill the earth and rule over creation is restated, albeit with new challenges because of sin.
the Lord provides “garments of skin” as a sign of freeing Adam and Eve from part of the burden of daily provision so that they can focus on their deeper calling.
the way to the tree of life is barred so that the hope-filled promise is guaranteed: sin is temporary and will finally be dealt with one day.
Adam signifies their belonging and hope and the acceptance of their reaffirmed calling by renaming the woman “Eve.”