The name Orpah (hpru) is from the noun [ru (“back of the neck”) and the related verb (“to turn one’s back”). The name Ruth (twr) is from the noun twur (“friendship”), derived from the root ur (“friend, companion”). Ironically, Orpah will eventually turn her back on Naomi, while Ruth will display extraordinary friendship as her life-long companion (see 1:14). Since they seem to mirror the most definitive action of these women, perhaps they designate character types (as is the case with the name Mara in 1:21 and Peloni Almoni in 4:2) rather than their original birth names.
Orpah has usually been considered as a derivative of the root 'rph, of which the noun 'oreph ("neck") occurs several times in Hebrew as a figure of apostasy (Jeremiah 2.27; 32.33); but a derivation from a root 'phr (with metathesis), resulting in a meaning "mountain-goat," has seriously been proposed.
As to Ruth, much has been deduced from the Syriac spelling found in the Peshitta re'ut, but elision of an 'ayin cannot easily be explained. A connection with a root rawah ("saturate, refresh"), as proposed by A. Bertholet (in Marti's Kurzer Handkommentar zum AT, 1898, ad loc.), is very doubtful, as well as a connection with Chaldaic werad ("rose"). The suggestion has even been made that the reversed reading of the name Ruth, tur, meaning "turtledove", may be of significance! (Hertzberg, ad loc.) However, J.J. Stamm favors "refresh" in "Hebräische Frauennamen (Hebräische Wortforschung, pages 325-326).