Hoi, Dutchie!

People from NYC are so proud of the fact that they were a Dutch colony once.

I wouldn't be so sure of that. I've been a New Yorker my entire life and not once have any of us ever amongst ourselves talked about being a former Dutch colony. It's not a particular source of pride by any means. It's just "Oh, we were once a Dutch colony."

They recognise that you are Dutch way more often than anywhere else in the USA

That's because we're pretty cosmopolitan and hear people speaking foreign languages all day and we get curious and ask.

[...] and every time they do you'll get a history lesson on how NYC started as a Dutch colony even though in the history of NYC it really wasn't that long.

That's because we have a lot of places that are Dutch in name--the Van Wyck Expressway, Brooklyn, the Bronx, Amsterdam Avenue, New Utrecht Avenue, Onderdonk Avenue, etc. It's just a thing that people who are relatively aware of things notice... "Hey, why does that street have this name?" etc.

NYC loves you back though. :)