Using local council areas, in 1996 there were three Ayrshire councils created which were North (Largs, West Kilbride, Three Towns, and the former Cunninghame District around Irvine, Arran), East (Kilmarnock, Loudon, Carrick), and South (Ayr, Carrick, Doon Valley).
There is no West Ayrshire at all, or if there was, it would be in the Irish Sea.
Regarding New South Wales, remember that it was created when we invaded, took over, colonised, and displaced the indigenous population i.e. the Aborigines, and carved up the lands by drawing straight lines on the map. Australia being south from Great Britain, a New North Wales would not have made sense at all assuming emphasis is on the first two words i.e. New South.