My payroll has the correct account and routing number but the wrong bank name. how do I move those checks into the correct check register?

Hello there, @ricfros!

You can update your bank account from the Payroll Settings so the checks will be posted into the correct register. But please know that only, that only the future paychecks will be posted into this register, moving the old ones is unavailable.

1. Go to the Gear icon.
2. Under Your Company, select Payroll Settings.
3. On the Bank Accounts section, select Company.
4. Select the account you wanted to post the check into.
5. Click OK.

In addition, here's an article you can read to learn more about the payroll bank account: Change bank account information.

Lastly, I've got you this helpful article for ideas about how you can manage your payroll transactions: Employees and Payroll Taxes for QuickBooks Online Payroll.

If there's anything else that I can help you with, please let me know in the comment section down below. I'll be always around ready to help.