The NHL requires the team to continue to be called the New York Islanders and stick with its logo featuring a map of Long Island. Mayor Bloomberg predicted the move will help the struggling Islanders, who have not made the playoffs since 2007 and last won the Stanley Cup in 1983, “get their mojo back.” “Never in my wildest dreams did I think we would be home to both the Brooklyn Nets and the New York Islanders,” said Brooklyn Borough President Marty Markowitz.