Interesting! It is privately owned, split by the surrounding properties. Possibly it has public access? Apparently it's called Heights Park and is one of the craters of Ōhuiarangi / Pigeon Mountain. See https://en.wikipedia.org/wiki/Pigeon_Mountain_(New_Zealand)

I would suggest leaving it as park, with a survey to confirm its name and whether it should be access=private, permissive or yes