Ms Ardern said the couple had struggled for months to decide on a name but had made a decision to wait until their baby was born to see which one suited her.
Niamh, as it is traditionally spelled, is a name from old Irish mythology, meaning radiance or brightness, but the new parents chose to go with the simpler, modern spelling to avoid a lifetime of people tripping up over it. "And when we met her, we thought she looked like she suited the name".
Ardern answered questions with a broad smile while rocking Neve back and forth as she slept.
"Te Aroha. was our way of reflecting the amount of love this baby's been shown before she even arrived".
"We're not placing any great expectations on this little baby except for happiness and love", she said.
But Ms Adern, who is only the second elected world leader to give birth while holding office, mixed up her English counties, as she thanked the royal well-wishers. It's such a rare event, in fact, that the last time anyone can remember it happening anywhere was in 1990, when Pakistan's then PM Benazir Bhutto popped out a baby.
"It's a real pleasure to introduce our little one to you all and to New Zealand", Ardern said on Sunday, thanking both hospital staff and members of the public for their "kindness, warmth and care" over the course of her pregnancy.
Priest filmed slapping child during baptism
Orthodox baptisms are usually done "forcefully" but many online commentators have criticised the priest's rather rough approach. Ohlalalala! I will scream louder than you. "I'm trying to figure out why no one slapped the old man back", one person said.
Since the birth on Thursday, Ms Ardern has been inundated with messages and gifts from world leaders, including the Queen and the Duke and Duchess of Sussex, who have sent a handwritten note saying they look forward to meeting later in the year. "And just figure things out as we go".
She and partner Clarke Gayford have named the little girl Neve Te Aroha Ardern Gayford.
"We've gone for simplicity, because Clarke with an "e" has caused all sorts of problems, and Jacinda with a "d", she said.
Her deputy Winston Peters is now acting prime minister, although Ardern will continue to be consulted on significant issues.
"Welcome to our village wee one", she captioned the photo. "So, I'm dying to see it and hold her and just see what's she's like".
Ms Ardern, who described herself as doing well but being "sleep-deprived", plans to take six weeks off work before Mr Gayford takes on the bulk of the parenting duties.
"It's just something really lovely in a world where so much is unfair that we're all very excited about it", said Frances Gerbic, a music teacher living in Auckland.