It's because shops were traditionally named after the people who owned them. There are still loads of shops bearing people's names, even now.
"Sainsbury's" supermarket used to be "J. Sainsbury's" named after its founder John Sainsbury, &c. "Morrisons" was "Wm Morrison" founded by William Morrison. So when you refer to a shop you say Sainbury's as in [Mr.] Sainsbury's shop, or "Morrison's" as in Mr. Morrison's shop.
Then this becomes so ingrained it gets misapplied sometimes. I don't think I'd ever say Asda's though. But I would say Tesco's, even though Tesco is the initials of three people.
It is this grammatical "mistakes" that make it so obvious a scam is a scam. I often raised my eyebrows at phishing messages and wondered if they knew grammar, but then realized in Nigeria this is their most appropriate grammatical structure and language begins with "Dear Sir..."