A Horse With No Name

A discussion of when we should capitalize the word "god" (when it is a name), led me to thinking about my visit to the No Name Cafe in Sausalito on Sunday. The name of this cafe is not "No Name." It just has no name. So I guess it should be called the no name Cafe. It turned out to be a bar without a kitchen. You can order food successfully--they send out to nearby deli. Obviously it isn't a cafe. What should I call it? (I may be caught in a loop on a horse with no name.)