Eve is from the Hebrew Chavah (חַוָּה) — from the root chai (life) — "to breathe, to live." The biblical Eve — the first woman, fashioned from Adam's side in the Garden of Eden, mother of Cain, Abel, and Seth, and through her sons the ancestress of all humanity (Genesis 2-4). "And Adam called his wife's name Chavah, because she was the mother of all living" (Genesis 3:20). Her conversation with the serpent and the eating of the fruit of the Tree of the Knowledge of Good and Evil is among the most painted scenes in Western art — by Michelangelo, Dürer, Cranach, Masaccio, and Klimt. Eve in mitochondrial genetics — "Mitochondrial Eve" — is the matrilineal most recent common ancestor of all living humans, who lived in Africa approximately 155,000 years ago.
Eve does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Eve reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.