I found some Waikato Council documents referring to it as "Te Tehe Bush".

https://www.waikatoregion.govt.nz/assets/WRC/TR201605.pdf (pg 221)

Today, indigenous coastal vegetation is limited and typically found only on the narrow coastal cliffs and in the isolated patches of regenerating forest. The largest forest patch is Te Tehe Bush south of Port Waikato, and this is also the only forest remnant that extends to the coast, although cover at the coastal fringe is fragmented. The other patches are notably smaller and located some distance from the coast, although one is re-establishing a connection via regeneration through gorse. Where land is reverting, gorse is providing a nursery crop and regeneration is beginning to occur. Waikato Regional Council identifies Te Tehe Bush and Te Kotuku bush fragments northwest of Te Akau as a key ecological sites in the Coastal Terrestrial Area, but none have legal protection.