self checkouts already have eye level cameras and they know which items you actually purchase so really not that farfetched to assume they're also using beacons to track your phone as well.
And when you swipe your card to check out they have your name, even if you don't use a loyalty card. Name + Face, along with some bluetooth tracking data. They can now track you forever, even if you delete the app, stop using your credit cards, etc.
From your link, it looks like "Name" is in Track 1:
Start sentinel — one character (generally '%')
Format code="B" — one character (alpha only)
Primary account number (PAN) — up to 19 characters.
Field Separator — one character (generally '^')
Name — 2 to 26 characters
...
There is one store in my neigbourhod where the payment terminals show this field (my full name) on the screen during checkout. I was very surprised when I noticed this the first time.
But apparrently not all card issuers fill the field with correct data. One card, a prepaid Visa from a big fintech, has "N/A" programmed in the field.