When booked directly with NZ you can do this. You may even be able to do this online although sometimes I find the price is more than the fare difference so end up calling.
When booked through a travel agent the travel agent wanted to charge me fees when Air NZ didn't! In general I've been referred back to the travel agent for changes. Only after the 1st flight of an itinerary was taken would Air NZ then takeover and I could liaise with them directly. I've largely taken over my own bookings so haven't been in this situation for a while.
I would try your luck though.