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Translation of Genesis 3:20
Adam named the name of his wife "Eve" because she was mother of all living.
Adam named a name for Eve only after the fall. There were no necessity to name Eve before the fall when Adam named names for animals, because Adam and Eve were one whole and didn't need to call each other by name.
After the fall Adam became too much human-centric: He calls Even as mother of all living, despite that humankind is not all living.