“Terrace names” are pretty common elsewhere too - see for example what the OS has for “Ingleton Road” in Chesterfield: http://ris.dev.openstreetmap.org/oslmusicalchairs/map?osl_id=399567 . OSM only has the terrace names because that’s all that’s visible on the ground from the western street: http://www.openstreetmap.org/#map=17/53.21838/-1.41860 .

A slightly different problem to the one that you’ve got is different names on the left and right of the street like http://www.openstreetmap.org/way/23987692 . At least there there’s a somewhat settled solution - name:left and name:right (also see https://map.atownsend.org.uk/maps/map/map.html#zoom=19&lat=53.047455&lon=-1.31546 ).