Which passport to use immediately after naturalisation?

What she needs to do is to report her marriage and name change to the Korean Embassy and have a new Korean passport issued with her new name. Irregardless of the dual nationality issue, her name changed at marriage and needs to be updated on her Korean documents (passport, DL, etc).

As long as her two passports have different names, travel between the two countries will be problematic. Once the names are the same she can use whichever passport suits her travel needs best.

My question is: the next time she exits New Zealand to go back to Korea, what passport should she use?

The easiest way to do this is the following:

• Book the tickets using her Korean name. Because she will use both passports (and therefore both names) at different times during travel, her Korean name is the only one that appears in both passports (as you said, in her NZ passport as an annotation). If there is any question during airline checkin, she will have both passports with her.
• Carry both passports during travel.
• When checking in for the NZ->S.Korea flight, show the airline agent the South Korean passport.
• New Zealand has exit passport control after airline checkin, so show the New Zealand passport here.
• When entering South Korea, show the South Korean passport.
• When checking in for the S.Korea->NZ flight, show the airline agent the NZ passport.
• When re-entering New Zealand, show the New Zealand passport.

This will allow her to stay in South Korea for as long as she wants, because she entered as a South Korean citizen. Similarly, upon return to New Zealand, there will be no question about how long she intends to stay because she has a New Zealand passport.

Showing the airline agent that she holds the passport of the destination will ensure that they will let her on the plane without questions about return tickets etc.

Most countries let their nationals leave and enter with very little requirements beyond holding some form of ID. There was and is such a thing as an exit visa in some parts of the world or countries that do not readily issue passports to limit emigration (historically, it was in fact a passport’s main purpose) but I would be very surprised if that was the case of New Zealand.

Since your friend is now a New Zealand citizen, she cannot possibly be an illegal immigrant in New Zealand and can stay as long as she wants in the country. Leaving with the same passport for the sake of ensuring that records are correct is therefore not very important anymore. In fact, if she uses her New Zealand passport, she will not get a stamp unless she asks for it. Passports are not stamped on departure in New Zealand in any case.

On the other hand, when flying back to New Zealand, she will need to convince the airline that she has the right to enter the country. That’s most easily done by showing her New Zealand passport but she would need to make sure the ticket was booked under her new name to be able to match it to the passport.

The “enter and exit a country with the same passport” rule is not absolute. It’s mostly for if you’re visiting a country for a short visit, for entry/departure tracking purposes.

In this case, where she naturalized, it’s not only possible but expected of her to enter and leave New Zealand with a New Zealand passport, because she is now a New Zealand national. New Zealand will no longer be concerned about matching her entry/departure records because she is no longer a foreigner.

Also, according to Article 15 of the South Korean Nationality Law, a Korean national who voluntarily acquires another country’s nationality automatically loses Korean nationality. So strictly speaking her Korean passport is not valid and she cannot use it anymore.

You said she has a different name when she naturalized in New Zealand? That must mean that that is her current legal name, which means she changed her name somehow. With whatever documents proving her change of name, she probably could have gotten some annotation on her Korean passport showing the new name. But that is moot now.

My suggestion is to use only the New Zealand passport for the trip and book the flight tickets with the name written on the New Zealand passport.

New Zealanders don’t require a visa to visit South Korea (90 days).

The only problem is her dual citizenship situation, New Zealand allows dual citizenship without issues, South Korea has some limitations on this topic, depending on her situation, when and how she acquired the New Zealand citizenship, she can still be a Korean citizen or not.