The reason sites put the logos up and ask the user to select is because VISA, MC and others either require it or give slightly better rates when you do.
How do you tell if a credit card is a Visa or Mastercard?
The First Six Digits
Each major credit card network has its own MII: American Express cards always begin with the number 3, more specifically 34 or 37. Visa cards begin with the number 4. Mastercards start with the number 5.
Why do they ask for name on credit card?
“Name on card” matters as eCommerce sites use it to prevent fraud. By asking for the “name on the card”, online shopping sites are including an extra security measure to minimize the chances of credit card theft, fraud, and scams.