eve (n.) Look up eve at Dictionary.com
c.1200, eve "evening," especially the time between sunset and darkness, from Old English æfen, with loss of terminal -n (which, though forming part of the stem, perhaps was mistaken for an inflection), from Proto-Germanic *æbando- (cognates: Old Saxon aband, Old Frisian ewnd, Dutch avond, Old High German aband, German Abend, Old Norse aptann, Danish aften), of uncertain origin. Now superseded in its original sense by evening.

Specific meaning "day before a saint's day or festival" is from late 13c. Transferred sense of "the moment right before any event, etc." is by 1780. Even (n.), evening keep the original form.
Eve Look up Eve at Dictionary.com
fem. proper name, Biblical first woman, Late Latin, from Hebrew Hawwah, literally "a living being," from base hawa "he lived" (compare Arabic hayya, Aramaic hayyin).
Like most of the explanations of names in Genesis, this is probably based on folk etymology or an imaginative playing with sound. ... In the Hebrew here, the phonetic similarity is between hawah, "Eve," and the verbal root hayah, "to live." It has been proposed that Eve's name conceals very different origins, for it sounds suspiciously like the Aramaic word for "serpent." [Robert Alter, "The Five Books of Moses," 2004, commentary on Gen. iii:20]