’ve done that without knowing account numbers. I’ve called utility companies, cable, phone, etc., then told them I want to pay one month on an account, and then given the name and address, and my credit card number.
To my surprise, I was told by two of the utilities that people do that all the time for others. I am guessing it’s parents paying off kid’s bills or vice versa, but it was still a surprise.
Just make sure you are only paying one month (if that is your intention), otherwise you might wind up getting debited every month.