NZ PM Jacinda Ardern reveals baby daughter's name

New Zealand Prime Minister Jacinda Ardern is heading home after giving birth and has revealed her baby's name.

Jacinda Ardern, New Zealand Prime Minister and her partner Clarke Gayford with their new baby daughter. Source: AAP

New Zealand's prime minister has introduced the public to her daughter and revealed the newborn's name.

A beaming Jacinda Ardern and partner Clarke Gayford on Sunday greeted media for the first time since arriving at Auckland Hospital on Thursday.

The 37-year-old began by announcing the baby would be called Neve Te Aroha Ardern Gayford - or Neve Gayford for short.

Jacinda Ardern holds baby daughter Neve Te Aroha Ardern Gayford. Source: AAP

"When we met her we thought she looked like she suited the name," she told reporters.

"Also it means, in various forms, bright and radiant and snow, which seemed like a good combination for Matariki (Maori new year) and for solstice."

Aroha in Maori means love and Te Aroha is also the name of a mountain near where Ms Ardern's family come from.

"Te Aroha was our way of reflecting the amount of love this baby has been shown before she arrived and all of the names we were gifted along the way (by various iwi)," Ms Ardern.

She and Mr Gayford had opted to spell the name Neve - as opposed to Niamh for example - for simplicity.