There isn't an option to change the Accounts Payable under the Account column if we're talking about a check made as a bill payment.
A workaround I can suggest is for you to delete the bill and the bill payment check transaction. You can then recreate a regular check, so you can use the account that you want, and it's the same account that will appear on the check register.
If you encounter a situation where a bill remains unpaid even after writing a check for it, visit this article for the list of solutions for this issue: Bill shows as unpaid after writing a check in QuickBooks Desktop.
I'll be around in case you need further assistance. Place a comment below, and I'll get back to you.