The name Ruth in the Bible
Ruth was the Moabite wife of Mahlon, son of Elimelech and Naomi of Bethlehem. Their other son, Chilion, married Orpah, also of Moab. When the men die, Ruth and Naomi move back to Bethlehem, where Ruth marries Boaz. In order to do so, Boaz appeals to the Leviratic Law, which dictates that when a man dies childless, his brother is to marry his widow and sire children in the name of the deceased man (Ruth 4:10, Deuteronomy 25:5).
Ruth and Boaz become the parents of Obed, the grandparents of Jesse and the great-grandparents of David, the great king of Israel, and finally the ancestors of Jesus of Nazareth (Matthew 1:5, Ruth is spelled Ρουθ, Rhouth in Greek). Strictly speaking, therefore, Jesus was not only a son-by-law of Joseph, he was also a son-by-law of Mahlon and not of Boaz.
Etymology and meaning of the name Ruth
There's no such word in Hebrew as רות (rut), and scholars don't agree where it may come from. One theory leads to the rich root-group רעה (ra'a I, II & III):
Scholars who follow this root group see the name Ruth as a feminine derivation of the root רעה (ra'a II), meaning to associate with, or be a friend of. And thus, they say, the name Ruth means (Lady-) Friend or (Lady-) Companion. The learned body behind the NOBSE Study Bible Name List agrees and reads Female Companion for a meaning of the name Ruth.
The valiant Alfred Jones (Dictionary of Old Testament Proper Names) proposes a different etymology and goes after the root ראה (ra'a), meaning to see:
Specifically, Jones sees the name Ruth (רות) as a contraction of the noun ראות (re'ut), meaning look. Hence, for a meaning of the name Ruth, Jones reads Beauty.
There's no telling whether to an ancient Hebrew audience the name Ruth sounded like Female Friend or Beauty, but all-in-all Ruth is quite a name.