Adam is an entry in the Oxford English Dictionary (the definition begins: The first human in the biblical account of the creation of the world), the phrase Adam and Eve is both a noun entry (meaning a) various plants b) origin, starting point and c) a style of cooking eggs) and a verb entry (Cockney rhyming slang for 'believe'), and Eve-like is an entry in the Dictionary (defined as 'Resembling Eve or her characteristics'). Eve herself, interestingly, does not have an entry in the OED.
Adam has a Hebrew origin. It originally had a generic meaning - human being or man. Most sources say that Eve, too, comes from a Hebrew root - meaning living or breathing.