umbrella cover

noun2

1. •
   A protective sheath used to contain a folded-up umbrella when not in use.
2. •
   (no longer used) The waterproof material that forms the protective upperpart of an umbrella (separate from the stick and ribs).

   • Her dress was as plain as an umbrella-cover, and she turned round without a word and preceded me into a waiting-room. — 1899