Rejected names: Shitter Shields, PeePee Panels.

Scranton Products offers "the most durable, low maintenance and best looking partitions, lockers and industrial sheet products in the industry," including their world-famous toilet stall partitions—the Hiny Hiders® (It is SO register-marked. Don't you even think of stealing it, General Partitions.) Though, "Hiney" does seem to be the preferred spelling of this naughty, informal word. Add your rejected names in the comments, if you want.
(thanks to Burns for the tip)
previously:
• there's pee in your butt.