I know it's a myth, but I wonder: did the myth become widespread because of the scene in The Godfather Part II where Vito changes his name to Corleone at Ellis

I know it's a myth, but I wonder: did the myth become widespread because of the scene in The Godfather Part II where Vito changes his name to Corleone at Ellis Island? Or was the myth already widespread, and the moviemakers got the idea from the myth?