Residents of Brooklyn have been called many things over the years: thugs, hopeless nostalgists, heavily accented bigots, and, much more recently, hipsters and arrivistes.

But it has been a century or more since anyone really called people in Brooklyn “islanders.”

Yes, the borough is on Long Island. Any map will confirm that fact. But while many in Brooklyn are thrilled to add a pro hockey franchise after getting the N.B.A.’s Nets, they wonder whether the Islanders’ name should be imported from Nassau County as well.

“If they’re not on the Island, why would you call them the Islanders?” said Peter Dunadee, 61, as he sat inside a car service dispatch station in Bensonhurst. “How about the Americans? That was a common name around here when I was playing roller hockey as a kid.”

“How about the Brooklyn Kings, for Kings County?” asked Billy Gordon, 64, a driver standing near him.