That's because you're not going to Tesco the registered company, you're going to (one of) Tesco's (shops). It's just traditional and logical grammar, not misnaming.
You may not be wrong that people do say it, I'm sure people say pretty much anything, across this vast planet. Yet people use double negatives, when meaning the negative too. Doesn't make it right.
I think language is defined by real-world usage, not by the logical structure that we theorise underpins it. If so, double negatives actually are right, or at least they can be, if they successfully communicate meaning.
Interesting observation ! Might it be because Tesco and Costa resemble ordinary names, and therefore easily appear in a possessive form ?
Or it might be about imaginary hierarchy. There could only be one actual duly-anointed king of burgers, but if one were to use the definite article to mark this, saying "I am going to the Burger King's", it would imply firstly that the king of burgers does actually exist, and possibly also secondly that he has but one solitary burger outlet.
A grammatical construction not quite so jarring when used with (say) "Tesco".
Pasting my reply to someone else rather than rewrite the same thinking:
I agree it's not consistent, but who ever accused English of being that?!
My point isn't that all business names are treated that way, just that the ones that are the reason is grammatical tradition not (for the most part) people who incorrectly think the shop is called "Tesco's" or whatever.
(But as others have replied to you, it's also more common than just Tesco, definitely including "Costa's" for lots of people.)
I agree it's not consistent, but who ever accused English of being that?!
My point isn't that all business names are treated that way, just that the ones that are the reason is grammatical tradition not (for the most part) people who incorrectly think the shop is called "Tesco's" or whatever.
I agree swores. Your comment did say 'traditional' and my comment was facetious.
There's been an historical transition from small chains owned by individuals (e.g. the Victorian Mr John Sainsbury) to big brands (e.g. Superdrug), hasn't there.
The possessive apostrophe was appropriate for the former but surely less so nowadays. I would guess "Sainsbury's" was a rebrand intended to reflect tradition.
I say Sainsbury's because the name is exactly that. I don't say Tesco's because the name, as you say, is Tesco. I would guess those who say Tesco's (and maybe Asda's) are just getting confused because of Sainsbury's.
We love apostrophes so much we have them on our supermarkets. If they're not there we add them.
e.g. I'm going to Sainbury's
e.g. I'm going to Tesco's
...despite the fact that it's real name is plain old Tesco.