What is the name for a piece of material that displays the logo or title of a specific show?

The correct term for a piece of material that displays the logo or title of a specific show is referred to as a show cloth. This is typically a large piece of fabric that is prominently displayed in front of a stage or at the entrance of a theater, serving both promotional and decorative purposes. A show cloth effectively communicates the identity of the production to the audience before they enter the performance space.

The other options do serve different roles in theatrical productions. A fly banner usually refers to a lightweight banner that is flown above the stage area, often changing during the performance. A backdrop is a large painted or printed piece that forms the background of the stage setting, providing context for the scenes but not specifically showcasing the title or logo. Illuminated signage involves signs that are backlit or lit from within, often used for visibility but not typically used to convey the name of the show specifically. Thus, the show cloth is the most accurate term for the item that prominently features the title or logo of a production.