The Rob Roy gets it's name from an opera by the same name which opened in New York in 1894. In those days it was common to bring about new cocktails and name them after popular shows. For the Rob Roy, they simply took an existing popular cocktail, the Manhattan, and substituted the rye for scotch. Most likely, it would have typically been made with Dewar's blended scotch, which had just recently begun being imported into the states.
David Wondrich has dug into the details of the Rob Roy and his research would indicate that it originated around 1895, in Hoboken New Jersey at "Duke's House". A salesman for Usher's Scotch Whiskey, when faced with an invitation to drink Manhattans, asked the bartender (Henry A. Orphal) to mix up something with Usher's whiskey instead. He swapped out the American whiskey for Scotch, and christened it the Rob Roy. ("Piecing Together the History of the Rob Roy Cocktail")