The information that we transact is a PAN—the 16-digit number—and the date, time and the amounts. We don't hold cardholder information. Your issuing bank does.
We see just that the 16-digit number did a thing. The merchant asks, “Can the 16-digit number pay for it?” We ask the issuer. We don't actually know the cardholder, but the issuer knows the cardholder. The issuer says, “Yes. That 16-digit number that belongs to Matthew can pay for that”, and then we pass that information back to say, “Yes, they can pay for it”. Then a charge goes back.
It's all information that passes from one side to the other. Depending on what you're asking for....