Satan says their eyes will be opened and they will be like God. When they eat their eyes are opened and... they know they're naked. The form of the words tells us: Satan lied.
God does not question the serpent when the woman blames him. He gives man a chance to repent, but not the serpent.
Adam names Eve "woman" before the fall, and "Eve" after the fall. Not sure exactly what that means. Maybe that good husbandry of the woman takes twice as much work as of creation?