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The 1 NEWS Colmar Brunton poll showed 32 per cent support for the name change and 61 per cent opposed - mostly older New Zealanders, National and Act Party supporters.
The remaining 7 per cent did not know.
Ahead of Te Wiki o Te Reo Māori (Māori language week) last month, Māori Party candidate for Waiariki, Rawiri Waititi, announced the party's policy for te reo Māori.
The policy set out to ensure New Zealand's name is changed to Aotearoa and that all Pākeha place names, cities and towns will be replaced with their original Māori ingoa (name) by 2026.
NZ First leader Winston Peters called the policy "headline hunting".
"This is plain headline hunting without any regard to the cost to this country," Peters wrote on Twitter.
"It will make our international marketing brand extraordinarily confusing when exports will be critical to our economic survival."
Peters went on to say the Māori Party was "again rushing down the path of separatism" instead of focusing on jobs, housing, health and education.
Prime Minister Jacinda Ardern did not say whether she supported an official name change, but told media she was seeing "Aotearoa" used more often.
"I hear more and more often the use of Aotearoa interchangeable with New Zealand and that is a positive thing," she said.
"Whether or not we change it in law I don't think changes the fact that New Zealand is increasingly referred to as Aotearoa."
She had not explored an official name change but was encouraged to see people use it more frequently.
Act leader David Seymour said now was not the time to argue about a name change.
"I don't care if we call it Timbuktu right now.
"When we're on top of this crisis and the debt it's created, then we can debate the name."
Green Party co-leader Marama Davidson said the party supported a "public kōrero around the use of Māori place names".
"We're really pleased that Aotearoa is now in common use, including in the official name of our own party, and believe this widespread usage is something to celebrate," she said.
On 1 News tonight, National Party leader Judith Collins said she was happy with the name New Zealand.