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Prime Minister Jacinda Ardern stood alongside partner Clarke Gayford and cradled the 3-day-old baby girl as she slept soundly despite the 50-odd media present.
The family took time to thank well-wishers and share the name of their first child as they left Auckland City Hospital after the birth on Thursday at 4.45pm.
Ms Ardern, glowing with motherhood, said it was a pleasure to finally introduce their little one to New Zealand and shared the chosen name for the first time since the birth.
She said they struggled to decide on the name, but settled on Neve Te Aroha Ardern Gayford, with Ardern acting as a middle name and Gayford the surname.
"For a matter of months we kept a shortlist of names and we wanted to wait until the baby arrived to really see which one felt like it really worked.
"But we chose Neve because we just liked it and when we met her we thought she looked like she suited the name."
Ms Ardern said the name meant bright and radiant, as well as snow, which they thought suited the time of year — it being Matariki and winter solstice.
They chose Te Aroha in tribute to the amount of love the baby had been shown.