You can edit the Payee in the register even after it's reconciled. This will generate a message that warns you it could affect the balance of the account for future reconciles. The steps below will show you how:
Go to the register of the account that you've reconciled.
Find the transaction and click on it.
Select the Payee drop-down and choose the correct Payee.
Press Save, then hit Yes when the reconcile message appears.
Now you have the correct Payee listed on the transaction in your bank register. You 'll also want to make sure the transaction keeps an R in the checkbox of the registry to ensure it's reconciled.
Please let me know if this gets you back to business. I'll keep an eye out for your response.