I wasnt very clear, sorry. I expect the payment terminal backend to match my credit card ID to the phone number I input at the terminal when I elect to have the receipt texted to me. After that, I do not expect to have to supply any more data (eg at a second merchant using Square).

Clover seems to have trouble with this, and their solution appears to be to lean on me to install their app and use it to check in at stores to get some discount, in exchange for knowing data like my date of birth.