Are names rigid designators?

On Mount Desert Island in Maine, people refer to roads with the definite article. So what the street sign says is “Crooked Road” might be mentioned in a sentence as “He lives on the Crooked Road.” This is likely to be how many roads originally got their names, so Birmingham Road in Coventry used to be the primary road to take to get to Birmingham, etc.  At some point the reference became the “official” (under whichever authority) name for the road, and this status could remain even if a different road became the preferred thoroughfare (cf., e.g., Kripke on Dartmouth).  But does the use of the definite article just reflect a quirky regionalism in the statement of the name?  Or is it indicative of a different conception on the part of the locals w.r.t. names and descriptions?  I only wish I could get a grant and stay here longer to do more research.  Perhaps I could combine this with my planned game-theoretic analysis of the soft-shell/hard-shell demarcation equilibrium…