New Zealand is another interesting one. Our demonym is "Kiwi" from the bird. I guess technically it's "New Zealander", but I don't think I've ever heard someone use that.
People used to understand this, around the english speaking world, especially after WW2 .... however thanks to some bozo marketing arsehole who renamed what we called "Chinese Gooseberries" to "kiwifruit", which in turn became known as "kiwis" we've lost our national identity (at least in the rest of the world - declaring yourself a "kiwi" in the US is more than likely just going to get you stupid looks)
'New Zealander' isn't really demonym, since it's a noun rather than an adjective. 'New Zealand' is both the name of the country and the demonym:
'The Russian prime minister' -> 'The New Zealand prime minister' (but you can't say 'The Russia prime minister')
The New Yorker mayor also doesn't sound right, although that's the correct demonym according to Wikipedia.
Would it be possible that perhaps the demonym is the name of the people, a noun, while the adjective is another thing, that can happen to coincide with either the place name or the demonym or something else, on a case by case basis?
I had to explain this to someone recently, and I was surprised that no other country seems to have a voluntary demonym that is completely unrelated to the name of the place? In English anyway.
