As far as I know, modern cards don’t just send your CC info to terminals, they do some form of a cryptographic handshake (probably a pubkey signature or similar) which gets confirmed by your bank. I believe Caveman was talking more about online shopping, where you have to enter your card number, expiration date, CVC and often your name too.
I’ve run across a few sites that allow me to check out entirely through Google Pay or PayPal, but not many. I still don’t love the info going through Google, but at this point they already have all my information, so it doesn’t really make much of a difference at this point.
And of course for anything that needs to be shipped they are going to need a name and shipping address.
I would like to seeegally mandatory “guest checkout” options with protections on data use. They’ll need to keep some kind of invoice/receipt of the transaction, but it should be illegal to use it for any other purposes than order/purchase tracking for guest accounts.