New Zealand Prime Minister Jacinda Ardern and partner Clarke Gayford present their new baby daughter, Neve Te Aroha Ardern Gayford, at Auckland City Hospital.

She's only days old, but the prime minister's daughter, dubbed the first baby of New Zealand, has put wind in the sails of a small rural town. 

Te Aroha locals are chuffed that the country's most popular newborn has been named after "the town of love".

On Sunday, Prime Minister Jacinda Ardern introduced her baby daughter to the world as Neve Te Aroha Ardern Gayford. 

DOMINICO ZAPATA/STUFF

Prime Minister Jacinda Ardern says she grew up under Mount Te Aroha, which her daughter's name reflects.

Te Aroha was chosen to reflect the "love and generosity" shown to the newborn.

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But it's also to acknowledge Te Aroha, a Waikato town of around 4000, which Ardern's family is from. 

Neve Te Aroha Ardern Gayford, who was introduced to the world on Sunday, has put Te Aroha on the map, locals say.

"I grew up under that mountain," Ardern said on Sunday. 

Peter Roache, head chef of Te Aroha's Ironique Cafe and Restaurant, said it's put the town on the map. 

"I tell people I work in Te Aroha and they go where the hell is that?

"Now I won't have to tell them because it's all over the news." 

Roache was surprised at the middle name choice. But 'aroha' means love, which seemed fitting. 

"And you can't put Morrinsville as a middle name, eh?"

The town could be in for a spike in tourists, he said. 

He hasn't seen any business specials popping up around the town in celebration of the name yet, but expects that might change. 

"Give it a week or so.

"I was just going to put a Te Aroha breakfast on the menu today."

Matamata-Piako District Council Mayor Jan Barnes said it was a special name for a special little girl. 

Te Aroha is a beautiful place that few New Zealanders know much about, Barnes said. 

"This is highlighting rural New Zealand.

"And it's where Jacinda's roots are." 

Tui Pā Marae Te Aroha trustee Mapuna Turner said the name was a blessing for the town.

"Aroha is one of the greatest values of Māori culture. If someone is hungry, give them a kai. That's aroha."

Mount Te Aroha makes the town such a strong place of love, Turner said. 

"One of our ancestors ... he climbed the mountain to get his bearings and fell in love with it because he could see everywhere."

Ardern will be invited to Tui Pā Marae with her baby girl, Turner said.

While Turner said some people aren't happy with the idea of  a Māori name being gifted, Turner said that's outdated.

"They're still in the 1830's. No aroha there."

ABC Te Aroha Childcare manager Michelle Gaukrodger said everyone seemed stoked by the recognition.

"We obviously love [Ardern], being in education.

"So we're very proud. What a wonderful name to [give] your baby as well."

It was special that such a small rural town had been honoured, Gaukrodger said.

"People who live here were generally born here, raised here. And don't tend to move."

 - Stuff