There's no direct connection to New Zealand. The founders visited New Zealand at some point, and brought back a stuffed kiwi toy for their child. When naming the company, it crossed their mind and so they went with it[1].
Their offices are in Mountain View. I used to live around the corner from them.
[1]: https://www.kiwico.com/blog/2011/06/09/why-the-name-kiwi-cra...