Kokohuia comes from the name of the repo (swamp) which covered the area where the school now stands. One kōrero is about a battle that took place between Pāmoana from Operiki and Tutemangarewa.
Pāmoana defeated Tutemangarewa and the battle was over. When asked, 'Did any fall by your hand today?', Pāmoana responded 'Kōtahi tui nā Pāmoana koko Pāmoana'. This meaning, although he had slain only one man, that man had been the chief of Rauru.
When the chief had fallen, the battle ceased. 'One bird alone I brought to earth, the one and only that scattered the rest'.