How am I giving my identity to a street vendor when I pay without cash?
To a street vendor, you don’t. To any authorized government agency that have power to ask the street vendor about the transaction that happened, and the bank for your personal details linked to the credit card number, you do. Also to any interested party who can compile the information from numerous PII leaks.
When the payment terminal asks the EMV chip on your payment card for tag no. 5F20, it will be told the Cardholder Name [1]. That, in connection with your PAN [2], is a pretty stable identifier. (Not if you are using prepaid cards, obviously.)
What if I pay with my phone? That’s pretty common in the Nordic countries (Swish)
Apple/Google Pay also implement the EMV standards, so at least in theory, it shouldn’t make a difference. In practice, I don’t know and I can’t check, unfortunately. It’s possible that they chose not to implement this particular tag.
I did query the chip on my plastic MC Debit and it definitely reveals my name.