In 1803, it got yet another name - ADELE ISLAND - after the ship of the first discoverer. About 20 years later it was renamed LYDRA ISLAND by another explorer, then RANGER ISLAND after the London whale ship "Ranger". An American whaler May Mitchell decided in 1834 that it should bear his name and called it MITCHELL ISLAND.
But it wasn't until a year later it that it finally got the name it's known by today. Another American whaler, John D. Sampson named it after his vessel, the NASSAU. It's not known why that name finally stuck, especially as another whale ship which sighted the island the following year tried to rename it NEW-PORT ISLAND!