Neve, derived from the the Irish name Niamh, means “bright” or “radiant” and Te Aroha means “love” in te reo Māori.

She said she and Gayford had struggled “for months” over the name, but the right one became clear once the baby was born.

“Probably like everyone, we went through that struggle where we kept this shortlist of names and we wanted to wait until the baby arrived to really see which one felt like it worked.

“But we chose Neve because we just liked it, and when we met her we thought she looked like she suited the name.”

Ardern said the name Te Aroha was chosen as a reflection of the support she’d received from New Zealanders during her pregnancy, especially the Māori community.

“I thought how do I reflect the generosity, particularly of all the iwi who gifted us names – and Te Aroha seemed to be a way,” she said.

“Te Aroha was something we settled on quite early. It was our way of reflecting the amount of love this baby’s been shown before she even arrived.

It’s also a tribute to Te Aroha mountain, on New Zealand’s North Island, near Ardern’s hometown of Hamilton.

“It’s the place where all my family are from,” she said. “I grew up under that mountain.”

She added that anyone who thought Neve’s name was “particularly long” should look at her own “ridiculously long name” – Jacinda Kate Laurell Ardern. “I think I counted it out – it’s the same number of letters.”

Neve shares a birthday with Pakistan’s former prime minister Benazir Bhutto, who was the first female world leader to give birth during office.

The prime minister was set to leave Auckland City hospital on Sunday, after arriving early on Thursday. 

She also told media she hoped the “novelty” of having a prime minister give birth in office would soon wear off.

“I hope for little girls and boys that there is a future where they can make choices about how they raise their family and what sort of career they have, which is based on what they want and what makes them happy.”

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