This Navaid is one of two in the U.S. with the same name. Rome GA is the other (RMG) VOR with the same name.
It is named for a nearby unincorporated town which, in turn, was named after local geological formations that reminded early settlers of the ruins of another place. According to Oregon Geographic Names, it was named for some peculiar geologic formations that suggested the ruined temples of Rome, Italy.
The identifier reminds one of an auto and truck manufacturer, a type of property, and a rock and roll band! Real estate owned or REO is a class of property owned by a lender, typically a bank, after an unsuccessful sale at a foreclosure auction. The band REO Speedwagon took its name from the REO Speed Wagon, a flatbed truck and fire engine, manufactured by the REO Motor Car Company. ("R.E.O." are initials of the company's founder, Ransom Eli Olds, who also founded Oldsmobile, once a division of General Motors.)