I wasn't precisely sure, so I was going for the generic "Australian Aboriginal", which is actually spelled "name:aus" as it turns out.

https://wiki.openstreetmap.org/wiki/Australian_Tagging_Guidelines/Australia%27s_First_Peoples#Indigenous_Languages_and_Place_Names

It looks like the language is Noongar based on the local government who manage it acknowledging the Noongar people as the traditional owners of the land. So it should be "name:nys".

https://www.kwinana.wa.gov.au/city-life/facilities-and-public-spaces/venues-and-facilities-for-hire/honeywood-complex

I also put the name on the footpath instead of the building, whoops!