John Wesley on Genesis 3:20

God having named the man, and called him Adam, which signifies red earth, he in farther token of dominion named the woman, and called her Eve - That is, life. Adam bears the name of the dying body, Eve of the living soul. The reason of the name is here given, some think by Moses the historian, others by Adam himself, because she was - That is, was to be the mother of all living. He had called her Isha, woman, before, as a wife; here he calls her Evah, life, as a mother. Now, 1. If this was done by divine direction, it was an instance of God's favour, and, like the new naming of Abraham and Sarah, it was a seal of the covenant, and an assurance to them, that notwithstanding their sin, he had not reversed that blessing wherewith he had blessed them, Be fruitful and multiply: it was likewise a confirmation of the promise now made, that the seed of the woman, of this woman, should break the serpent's head. 2. If Adam did of himself, it was an instance of his faith in the word of God.