Earlier quoted context omitted.
> calling it Uno's isn't inconsistent with how we talk about Walmart's stores calling it Uno's isn't inconsistent with how we talk about Walmart's stores or Google's website No, calling it "Uno Corp's pizzeria" would be the equivalent. Nobody says they're "Going down to Walmart's" or "doing some research on Google's."
My grandmother would indeed refer to shopping at “WalMart’s” or “Penney’s”. Maybe a regional thing (she was from central PA)?
I can understand Penney's or Dayton's since those were people who founded eponymous stores. I suppose we have our answer -- people established a habit of the "S" when that type of naming was so common, and extended it instinctively to all stores even though there was never a Mr. Kmart or a Mr. Circuit City.
Fun tangent: I learned pretty recently that the southern California grocery chain is named after a man with the last name "Ralphs," so it never had an apostrophe and indeed shouldn't have one (in any language).