Named Afterwards Genesis 3:20

After the fall from grace, after Yahweh banishes Adam and Eve from the Garden, and they are doomed to suffer, sin, recover and die, at this point Eve receives a name. I am speculating, but being name makes one an individual, and one is only an individual if one thinks, and enjoys free agency of will. Eve, the sinful mother of humankind, has become real, flesh and blood. she has become an individual, a unique. Is the fall from grace a blessing more than a curse, more a gift from God than a punishment? I would think so. Here is that verse from my 1970 The American Bible: "The man called his wife Eve, because she became the mother of all the living." Here is this verse from the Holy Bible (KJV): "And Adam called his wife Eve; because she was the mother of all the living."