Previously Adam had called her Woman, his reason given then, and God's post-fall-pre-exile pronouncement gave Adam reason to exercise faith as to what her role would be.
Gen 2:22-23 Then the rib which the LORD God had taken from man He made into a woman, and He brought her to the man. (23) And Adam said: "This is now bone of my bones And flesh of my flesh; She shall be called Woman, Because she was taken out of Man."
Gen 3:16 To the woman He said: "I will greatly multiply your sorrow and your conception; In pain you shall bring forth children; Your desire shall be for your husband, And he shall rule over you."
Gen 3:20 And Adam called his wife's name Eve, because she was the mother of all living.