LoneWolf,
Adam gave Eve her new name shortly after they sinned and were cursed. Another speculation to add to yours is that he named her Eve out of his great remorse. The consequences to him were in a sense much worse than hers. He lost his immense honour and privilege of being the founder of the human race. Eve apparently understood that too. Later she said regarding the birth of Cain: "I have gotten a manchild with the help of the LORD." (Genesis 4:1) She gave no credit to Adam.
Later, after the death of Abel and the curse upon Cain, she seemed to see her world starting all over again with the birth of Seth. She said, "God has appointed me another offspring in place of Abel, for Cain killed him." Again, no mention of Adam. It seems she sees only God and herself in the picture.
Down until our day, the nurturing of children is done predominantly by their mothers. Even in the story of Jesus' birth, Mary receives far more attention than Joseph.
A new Adam has come into the picture, namely, Christ. Our re-birth through faith in his name brings us back into a relationship with God the Father as his sons and daughters.
Only those born of a woman can receive that special adoption by God. Perhaps to emphasize John the Baptist's unique relationship with God, Jesus said "Truly I say to you, among those born of women there has not arisen anyone greater than John the Baptist!" (Matthew 11:11) Jesus could have meant just as much in the context if he had merely said "among those born," but he added "of women" possibly for a profound reason.
In the Kingdom, Adam will have been forgotten. He will not be considered the father of all the living. Eve, however, will continue to be known as our first ancestress and mother.
Just some thoughts to add to yours.
fjtoth