Rhode gave her name to the island of Rhodes, of which she was a protector. It was the center of her cult. Her name stems from the pink hibiscus which was native to island and was similar to a rose, which is also etymologically related to her name
The first inhabitants of Rhodes were the Telchines. Helios created the island and, with Rhode, had seven sons (the Heliadae -- Ochimus, Cercaphus, Macareus, Actis, Tenages, Triopas, and Candalus) and one daughter, Elektryo. Elektryo died a virgin and the sons became well-known astronomers and rulers of the island.
Note: In Greek mythology, Rhode or Rhodus is a difference person than Rhodos.