Setting up a credit card account will not create a vendor name to pay. It's two different steps.
If you're writing a check to pay the credit card balance down, you can enter the vendor name in the check's Payee field and QuickBooks will prompt you to set up the vendor. Then use the new credit card account as the "expense" account on the check (even though the credit card account is not an expense account) and that should be all you need to do to create the payment.
