I am pretty sure there's a special term for it, because "paper cup of coke" doesn't sound right, and all of the other words I can think at the moment doesn't sound great. If it doesn't sound great, it's not great for marketing, so I am pretty sure there's a word for it.
Like when you order a Big Mac trio, you get coke, but I don't think the cashiers would call it "a cup of coke".