From Middle English warenne, from Anglo-Norman and Old Northern French warenne, from Old French guarenne, garenne, probably from a Germanic *warinne "game park", from the root *war- of Proto-Germanic *warjanÄ… (“ward off, defend against") (cf. also Old French warir, guarir, a borrowing from this Germanic root). Alternatively the Old French may have derived from a Gaulish varenna (“enclosed area"), related to varros (“post").
The given name used in medieval England and returned to use in the nineteenth century, often transferred from the the surname. It has been more popular in the U.S.A. than in the U.K.
Two different Norman surnames, one from a Germanic given name war(in) "guard", another from a place La Varenne "the game park" in Normandy.