In Ukraine we call it "kleenka" the same word for tarp, plastic sheet, plastic sheeting, waterproof cover, all-weather cover. We cover our tables with this. Plastic sheeting for covering hay looks and feels the same as the material table cloth made of, so we call it by material it's made off. We also have the word tablecloth, but it is made of textile. Do you also have another name for a tablecloth that is not textile?