I checked the NY Street GIS while it did have "Guymard Tpke" on the tiles, when I clicked on the segments it had "Unnamed Street".  The Guymard Turnpike is that public road off to the west with the U bend.  Since this is a private road, Guymard Turnpike is either an outdated historical name or a mistake. So naming it that would only cause confusion with the public road.

It's not uncommon for private property roads to just not have names.  Since surveying private property isn't something we can do and the very limited value this road currently has to anybody navigating, I have removed the name, added a noname=yes and consider it resolved.