They seem to be run by the local authorities rather than the Senedd centrally, so I guess they all do their own thing?

Gower doesn't even have its own website and is on Swansea Council's, while Llŷn has contact info for Gwynedd Council (both still AONBs)

https://www.swansea.gov.uk/article/9102/Gower-Area-of-Outstanding-Natural-Beauty

https://www.ahne-llyn-aonb.org/Contact

The only thing calling them NLs at this point is the NL website. You'd think the councils would have at least changed the words on their websites by now.