The island is named after Brent Clements Rodd, who had a long association with the island and the local area. He first attempted to buy the island from the government in 1842. The Rodd family, who lived on the western shore of Iron Cove in what is now the suburb of Rodd Point, used the island for recreation. Rodd tried again to purchase the island in 1859 and even put down a deposit of 17 pounds on it. However, the transaction was never completed and the island eventually became part of the first public recreation reserve in Sydney Harbour in 1879. Despite being a solicitor, Rodd managed neither to purchase the island, nor to have his deposit refunded.