Baby will receive her first bath Saturday afternoon and the PM's mother Laurell Ardern is also expected to visit.
The Irish name means "radiant" or "bright".
The "Ardern" would serve as another middle name, meaning the baby is known as "Neve Gayford", she added.
"The team were very generous in allowing us to hold onto her for quite a while before she had to be whipped away".
Ardern answered questions with a broad smile while rocking Neve back and forth as she slept. Te Aroha means "love" in New Zealand's indigenous Maori language, and Ardern said that name reflected the amount of love and generosity that people had shown the couple even before the baby arrived.
"Hopefully these things that in these moments now are.a novelty.one day they aren't new any more", Ardern said.
Prime Minister Ardern is the second world leader to give birth in office, and the first elected leader to take maternity leave.
Former New Zealand Prime Minister Helen Clark said the birth and the way the country had greeted it would be seen as inspirational by advocates for gender equality and women's empowerment.
"I think every new parent would probably reflect that", she said.
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"I do not want to create a false impression that all women should be super-human or super-women", she said recently.
Ardern gave birth in Auckland Hospital, the country's largest public hospital, with Gayford at her side.
Gayford tweeted the same photo of the happy couple and their newborn baby on Twitter, saying: "So happy to announce our little girl has finally arrived!"
Ardern is just the second elected world leader to give birth while holding office.
Ardern spoke briefly to media outside Auckland City Hospital on Sunday alongside her partner Clarke Gayford, revealing the name they had chosen was Niamh Te Aroha Ardern Gayford - or Neve Gayford for short.
Mr Gayford, a 40-year-old television presenter, will be the child's primary carer once Ms Ardern returns to parliament.
"We've gone for simplicity, because Clarke with an "e" has caused all sorts of problems, and Jacinda with a "d", she said. Deputy Prime Minister Winston Peters has taken the reins as New Zealand's acting prime minister.
She told Sky News: "We had been told that it was unlikely that we would be able to have a family without help".
"Those moments have mattered as much to us as any of those lovely messages of support from around the world", she said.