"She doesn't look like Jacinda as a baby because she's more tiny, more petite", Ardern's mother Laurell Ardern said.
The name has Irish origins, and means in various forms "bright", "radiant" and "snow".
Te Aroha is a rural town in the Waikato region of New Zealand's North Island, and is also the name of a Maori song about love and peace.
Ardern's partner Clarke Gayford spent Thursday night with Ardern at the hospital.
"We're not placing any great expectations on this baby - except happiness and love", she said.
Many in New Zealand and around the world had held up Ardern's pregnancy - just the second time an elected leader had given birth in office since Pakistan's Benazir Bhutto in 1990 - as a symbol of progress for women.
The Prime Minister's office (PMO) says the trio will depart Auckland Hospital shortly after.
"We chose Neve because we just liked it, and when we met her she just looked like she suited the name", she said.
Ardern and Gayford said they kept a shortlist of names before they settled on the two names that they thought best fit the newest member of their family.
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It's still the sport that I love with all my heart. "I definitely feel relieved that I won it and what a great week". Murray, 31, made his competitive return on Tuesday at Queen's, where he lost in three sets to Nick Kyrgios .
On Sunday, the little baby made her first public appearance at Auckland City Hospital, appearing to sleep soundly as her parents answered a few questions for waiting reporters.
AUCKLAND, NEW ZEALAND - JUNE 24: New Zealand Prime Minister Jacinda Ardern and partner Clarke Gayford pose for a photo with their new baby girl Neve Te Aroha Ardern Gayford on June 24, 2018 in Auckland, New Zealand.
Tweeting her congratulations to Ardern and Gayford earlier in the week, former NZ Prime Minister Helen Clark said their parenting arrangements were gender-equality in action.
Her deputy Winston Peters is now acting prime minister, although Ardern will continue to be consulted on significant issues.
New Zealand Prime Minister Jacinda Ardern has left hospital after giving birth to a baby girl. "We've gone for simplicity because Clarke with an "e" has caused all sorts of problems, and Jacinda with a 'd, '" Ardern said.
She will take six weeks of leave before returning to work.
Ardern said the family was doing well - but, as is common with new parents the world over, were sleep-deprived.
"Those moments have mattered as much to us as any of those lovely messages of support from around the world", she said.
She posted a photo to her Instagram account, saying: "Welcome to our village wee one".