Meaning: it could be a variant of Shunamite meaning "from Shunem", Shunem being a village or a small town mentioned a few times in the Bible, referring to someone who came from there.
I've also seen it as possibly being derived from Hebrew shalom meaning "peace".
According to Llewellyn's Complete Book of Names by K.M. Sheard the name could possibly be related to the name Shulmanitu, the feminine form of Shulmanu (also spelled Shulman) which is the name of the Mesopotamian god of fertility, war and the underworld, whose name is related to Akkadian šulmu meaning "health" and "well-being".
Shulamite is the name given to the heroine in the Song of Songs (also known as the Song of Solomon) in the Bible because she came from the village of Shunem; her real name is unknown. The Song of Songs is a celebration about sexual love.