Was the show called Gilligan's Island because it was his fault they were on the island? He clearly was not in charge nor did he have any rightful ownership claim on the island.
Actually, they got Tina Louise on the project by promising it would be called "Ginger's Island", and that Ginger would be the main character. She was bitter about that till her dying day, as it ruined her career as anything other than Ginger.