It always makes me laugh when I see this - a Kiwi is a small flightless bird native to New Zealand, and people from New Zealand are also often known as Kiwis.
Kiwi Fruit, as it's properly called here, is not native to New Zealand, and that's also not the real name of the fruit. It's actually a Chinese Gooseberry. New Zealand grows a lot of them and they started marketing them as Kiwi Fruit to make them sound more exotic and to point out the fact that they come from New Zealand.
