Anodyne

I like this name for a girl because: A) it's the name of my favorite all-time album and song (by Uncle Tupelo); B) it means something that soothes. For short, we would call her Ana, Ann or perhaps Annie.

Here's what Merriam_Webster has to say about Anodyne:
noun 1 : something that soothes, calms, or comforts 2 : a drug that allays pain
Latin anodynos, from Greek anOdynos, from a- + odynE pain; probably akin to Old English etan to eat 1 : serving to assuage pain 2 : not likely to offend or arouse tensions : INNOCUOUS