I think generally, if the customer is using an on-us check to purchase the cashiers check they will make the check payable to the bank (this is what I’ve seen most) or the customer themselves.
Our bank prefers the check be made payable to the bank, but if the check is made payable to cash or themselves we make them sign the back of the check being used.
I agree with Kathy, if the check is made payable to the customer it would need to be indorsed over to the bank. Like Kathy, payable to the bank is the preferred method.