St Leonards School principal Sarah Thompson said it was proposing adding Te Umukuratawhiti to its existing name.
She said it was "the name that Māori use to locate the area in the same way that the name St Leonards does".
However, social media reaction was mixed, many asking why consultation was open for only five days, why a name change was necessary and why the dual name was already present on the school’s website.
Ms Thompson said the new name was the best of both worlds.
"A dual name would ensure we continue to honour our school’s long-standing identity while also embracing the cultural heritage of mana whenua."
Some of the reasons for changing the name was to stop confusion they often got with another primary school in Auckland called St Leonards Road School, whose mail they often received.
Changing the name would also hopefully stop parents from making the assumption the school was religiously affiliated.
It would honour the Treaty of Waitangi and help all pupils feel as though they belonged, she said.
"We want our school’s identity to reflect all the narratives of our area — integrating te ao Māori alongside the other cultures that make our community unique.
"We view this as an educational journey to connect our students more deeply with the history of the land they learn on."
The new name was already being used informally with pupils in the school to introduce them to the local history of the area and the Māori language.
Pupils had all responded positively and respectfully, Ms Thompson said.
Public consultation closed on Monday.
"Community input is the cornerstone of this process, and we have been very encouraged by the high level of engagement — we are currently in the phase of listening and gathering all perspectives ... every voice is being heard as we consider our next steps."
It would not be the first time the school has changed names.
The first school on the current site opened in 1868 as Upper West Harbour School and had a roll of 21 pupils.
In 1874, the name was officially changed to St Leonards School.
