[Tennessee Nana]

No they don’t...

someone else dubbed New Zealanders as Kiwis...

I lived there 22 years and never called myself a Kiwi nor did my mother, father, grandmothers, siblings, aunts, uncles cousins etc ever call themselves Kiwis..

[PLMerite]

Then what do New Zealanders call themselves?

The NZ Air Force roundel has a kiwi on it:

[Osage Orange]

Interesting.....never would have thought that.

How did you end up here?

I've been to Auckland...and there are many places I might like to live there.

[Boogieman]

“someone else dubbed New Zealanders as Kiwis...”

Probably an Aussie :)

[DCBryan1]

I lived there 22 years and never called myself a Kiwi

Do you call yourself an Allblack?

[Ditter]

I have 2 cousin in NZ and they refer to themselves as Kiwis. One lives in Auckland , the other one in Christ Church. Maybe your family doesn’t but some do. As to who started it, I have no idea, I am a Texan.