Basically, the answer is that you can't do this. Here's why:
Online payees are payees to whom payments are sent, either through Quicken Bill Pay or through the bill pay service of a financial institution. Once you've created an online payee name and sent it to the bill pay service, you typically can't change the name (since that's how that payee is identified).
Downloaded transactions (Direct Connect and Web Connect), frequently contain payee names. For example, you may have made an online payment or some other electronic payment (for example with a credit card or ATM card) to that payee. The payee names contained in downloaded transactions are the names that the Renaming Rules feature is concerned with.
Depending on how your preferences are set, downloaded transactions are memorized and added to the Memorized Payee List as they are accepted into the register (or transaction list, for investment accounts). If you rename one of these downloaded payee names, Quicken updates the name in the Memorized Payee List and (optionally) adds renaming rules, so that the payee name is automatically renamed the next time it is downloaded.
If a downloaded name is the same as an online payee name, renaming it in the register and creating renaming rules doesn't affect the Online Payee List; the original online payee name is used to make new payments.