Thank you for improving the map.

I agree there is no evidence of the road having a name, but if I heard the name "Hopton and Carson Bypass" I would assume it refers to this road.

Maybe tagging it as a "loc_name" makes sense https://wiki.openstreetmap.org/wiki/Names#Local_names_(loc_name)

Have you considered asking Rufus Green who added this name in https://www.openstreetmap.org/way/39989117/history/13 ?