Making an anonymous payment is not difficult, but may require some research and legwork. Getting the appropriate account to make the payment to is probably the most difficult task, because companies will not usually give you account information unless they are authorized to by the account holder. You must also remember not to use a check or credit card because they both leave paper trails. Cash is also risky because it requires you to either chance being identified when you pay in person or risk losing cash in the mail. For true anonymity, a money order is your best and safest bet.
Identify the account number to which you want the payment applied.
Purchase a U.S. Post Office money order. Buy with cash to assure complete anonymity. Write the account number on the money order. Use the address if the payment is a rent or mortgage payment.
Mail the money order to the appropriate payment address. Do not include your return address on the envelope.
Keep your money order receipt in case there is any problem with the payment.
There is always a digital record with online transactions.