Interesting… apparently they are called Landau bars(automobile):
“In the 1920s and 1930s, especially in the United States, the term “landau” became used for a simulated convertible, in which a fixed roof of a sedan with solid rear quarters was covered with fabric or leather and fitted with side landau bars to make it appear like a convertible top. This became the commonly accepted definition of “landau” in North American usage thereafter.”
From the page on hearses: “More popular in the United States is the landau style, with a heavily-padded leather or (later) vinyl roof, and long blind rear quarters, similarly covered, and decorated with large metal S-shaped bars designed to resemble those used to lower the tops on some horse-drawn coaches.”