Ha! Newcomers!
Baltimore’s native beer, National Bohemian, has been called Natty Boh for a century or more. It’s not clear from my brief Googling when it started, but it definitely originated with consumers, not the company. And the company, while acknowledging the term, doesn’t see to have firmly embraced it officially. This sticker is the only Natty Boh product i could find on the official website. None of their clothes there seem to use it.
So I think Natty Boh meets the OP’s criteria.
You drink it and lose an eyeball?
Coca-Cola was trademarked in 1893. The nickname Coke wasn’t trademarked until 1945. For a half-century the company resisted using the nickname because they didn’t want their soft drink to be confused with the coke used in blast furnaces.
ISWYDT
I wondered if anyone would remember that. 
There’s a brand of malt liquor, Haffenreffer, whose bottles and cans designate their brew as “PRIVATE STOCK”.
I have had occasion to hang out with people who drink it (although I don’t greatly care for it myself). Nobody calls it Haffenreffer. It is always, invariably, referred to as Private Stock.
Magic Mountain in California became Six Flags Magic Mountain (no over). As I recall they were in bankruptcy over someone dying on one of the coasters because they were very overweight and the safety bar couldn’t be locked down and they flew off from a great height. Six Flags bought them out.
Maybe not totally in the spirit of the OP but how about The Dope?
That reminds me that Jackson Browne’s eponymous album was not called “Saturate Before Using”.
That “absolutely, positively” tag line is utterly embedded in corporate-speak even to this day. And is also heavily used in the transportation industry, usually ironically about some clusterf*** of delay and confusion.
It may well outlive FedEx itself.
How about Datsun turning into Nissan?
That’s funny! There was a marketing campaign where some 7-11’s briefly changed their name to Kwik E Mart.
Now I’m waiting to see if they actually change the signs on Japanese McDonald’s to WcDonald’s.
Datsun was a brand used by Nissan for exports to certain markets. The US was the main one but that brand was discontinued in 1986. (We had a car bought around that time that had both labels on it.) It was used again for some other export markets but is now officially dead.
Nissan has always been Nissan.
This thread made me look up two companies to see if they fit. But no in both cases.
Sears used to be known as Sears-Roebuck. The Roebuck got dropped on signage some time ago. Strangely, the company still goes by the full name. (They are down to 13 stores. So it will apparently officially end it’s life as Sears-Roebuck.)
I thought United Parcel Service officially changed it’s name to UPS. Again, no. Do they use the full name in any consumer oriented signage or ads?
Note that “Datsun” refers to an older car brand in Japan, the DAT. They changed their name with a new model that was the son of DAT – DATson. It later changed to Datsun.
In the Palms neighborhood of L.A. there used to be a marijuana dispensary using the name Kindness For Cures, which had taken over a former KFC location. They kept some of the letters, which must have inspired the name to begin with.
They’re still around, but now in a completely different neighborhood.
We might parse that as “Harrod’s Stores” → “Harrods” for short. Same with “Morrison Supermarkets” → “Morrisons”. No idea what the official explanation is; what do they have to say about it?
Vons, a large grocery store chain, was originally Von’s.
Back in college I knew the family that started Von’s. Mongo rich but nice folks.
That was the first word in their multi-word Dutch surname. So named not so differently that e.g. Smith’s Plumbing.
Once the family sold out the name was de-personalized.
I don’t recall calling VWs Beetles before the official name change, but I remember calling them Bugs. As in Slug Bug, the punching game (although for some reason, in my family, it was Bug Slug).
Another one: Freddies for Fred Meyer.
Not sure if this one really qualifies, but Lidl (pronounced something like lee-dl in Germany, where it was founded) was commonly prounouced ‘liddl’ in the UK when it came here; instead of trying to ‘correct’ this, they accepted it and ran with it - to the extent that their advertising uses the phrase ‘big on value, Lidl on price’ which sounds a bit like ‘Little on price’; they also named the homewares section of the store ‘The Middle of Lidl’ (which only works if it rhymes).
UK Retail chain Wilkinson rebranded themselves Wilko, after this name was already common usage. Marks & Spencer was commonly called ‘Marks & Sparks’, and although they did not adopt this for their primary branding, they did name their loyalty card ‘Sparks’.
The original was in Dallas. The competitor park in Houston was Astroworld, which if IIRC was bought out by Six Flags during the ‘90s. It was definitely still Astroworld when I went as a kid in the late ‘80s.
And the six flags didn’t include Great Britain. It was France, in addition to the others you mentioned. Texas was never a part of the British Empire.