ASV notes on Genesis 3:20-24
Adam gave name to his woman and called her Eve which means source of life or life giver because she was to give life to all the people that was to be born on earth. Eve died but her name was still Eve and she did not change it. She was now going to give birth to dead people, people without the spiritual connection to God’s spirit. People were “dead” but the name of Eve was still “the source of life.” In the gloom of death Eve still was a living prophesy, that one day the life would reappear and once again fill the hearts of people.
Now Adam and Eve had sinned but God still loved them and looked after them, He made them tunics of animal skins, God made tunics, not one tunic, but several. When God made the tunics, they must have been of first class quality.
In the middle of the garden there was another tree, the tree of life that had fruit with the everlasting life in them. The problem now was that if Adam and Eve ate from that tree also, they would live in their fallen state forever and fill the earth with sin and death for ever, no one would die and sin would develop in all its horror.
But God still loved them and all the people after them, therefore He blocked the access to the tree of life, the man and woman had to leave the garden.