Evelyn comes from the Norman French Aveline, ultimately a diminutive of an Old Germanic name meaning "desired" or "wished-for." It was originally a surname, then a male given name in the seventeenth century, before becoming firmly female in the late nineteenth.
In Pythagorean numerology the letters of Evelyn reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.