Holland doesn't exist as a nation state, in the same way Hawaii doesn't. Unlike Hawaii though, Holland is the influential region of the Netherlands and has a degree of proud independence. It's really a question of how people identify themselves.
I'm not sure what the American equivalent would be. The nearest I can come up with would be someone from Dallas identifying themselves as a Texan before they admitted to being American. You can bet your life though that if you went to Europe and spoke to someone, you'd pick the wrong the side. Europe is riddled with these
American Presidents still use the country name England to refer to the UK (albeit the present incumbent isn't the worst offender - that was Reagan)
Catalans, Basques and Castillion Spanish is another one
Walloons and Flems in Belgium
Italy has a north south split compounded by a history city states (Venice recently held a referendum to annex itself from Italy)
Come to think of it Scotland, is voting in the next few weeks for independence (well they're voting against independence as it happens - but we'll see)