Hello! It's not a direction sign, it's a black metal sign of the type used for path names. I'll take a photo next time I get a chance.

As for the naming, I meant that the name of the Walkway is currently tagged on the ways themselves (e.g. https://osm.org/way/23126655) in addition to the relation. If this path is indeed called "Easter Hailes Gate", then I would suggest that the ways should bear that name only, and the walkway name should be on the route relation only.