There are multiple origins and meanings for the name Eve:
1. Latinized form of the Hebrew name Hava. Comes from the Hebrew word (חַוָּה) [Hay] - "live, living, alive; active"
2. Derived from Greek word ευγενής [ewyenis] - "noble; polite"
3. Diminutive form of the given name Evangeline - "good news"
In Abrahamic religions Eve - mother of all people, Adam's wife, the mother of Cain, Abel and Seth. In Quran mentioned as Hawa.
Eve was, according to the Book of Genesis and the Quran, the first woman created by God, and an important figure in Judaism, Christianity, and Islam. Her husband was Adam, from whose rib God created her to be his companion. She succumbs to the serpent's temptation via the suggestion that to eat the forbidden fruit from the Tree of the Knowledge of Good and Evil, would improve on the way God had made her, and that she would not die, and she, believing the lie of the Serpent rather than the earlier instruction from God, shares the fruit with Adam. As a result, the first humans are expelled from the Garden of Eden and are cursed.