The name is derived from the Irish name Niamh, which means bright, radiant and snow, Arden told reporters at Auckland Hospital.
The "Ardern" would serve as another middle name, meaning the baby is known as "Neve Gayford", she added. "And when we met her, we thought she looked like she suited the name". Te Aroha was something we settled on quite early.
Her second name, Te Aroha, which means "love" in Te Reo Maori, one of the country's national languages, was a nod to the many Maori iwi, or tribes, that had offered names as a gift to Ardern while she was pregnant.
"Hopefully these things that in these moments now are.a novelty.one day they aren't new any more", Ardern said.
Ardern became New Zealand's youngest prime minister when she took office through a coalition deal a year ago after an inconclusive election, and now became the first woman in the country's history to give birth while in office.
The last leader to give birth while holding office was late Pakistani Prime Minister Benazir Bhutto, who had Bakhtawar in 1990.
A spokesman said the message Ardern referred to from Prince Harry and Meghan was a "lovely hand-written note" that looked as if it was written by Meghan.
US House votes to defeat conservative bill
Differences between conservative and moderate Republicans delayed a vote initially planned for yesterday. There were also signs that the administration was dialing back its "zero-tolerance" policy, for now.
In this photo released by the Office of the Prime Minister of New Zealand, Prime Minster Jacinda Ardern, left, and midwife Libby, no surname given, pose with Ardern's newborn daughter at the Auckland City Hospital in Auckland, New Zealand Friday, June 22, 2018.
On Friday Ms Ardern became the New Zealand's first female leader to give birth while in power.
"To everyone who sent anything, even just a comment on Facebook, thank you", says Ardern, before departing back up the corridor from which she had come. "So, I'm dying to see it and hold her and just see what's she's like".
The couple welcomed Neve, their first child, on Thursday, announcing the news on Instagram.
Mr Gayford, a 40-year-old television presenter, will be the child's primary carer once Ms Ardern returns to parliament.
"I hope for little girls and boys, that actually there's a future where they can make choices about how they raise their family, and what kind of career they have, that are just based on what they want, and what makes them happy".
While the day-to-day prime-ministerial duties will be handled by the polarising 73-year-old deputy PM Winston Peters, Ms Ardern will still be on call for any major decisions.