Not sure why you would allow it. Potential for fraud or other bad actors gaining access to the bank system is not worth it. If banks have name matching software, these will be automatically returned.
If the direct deposits are federal recurring benefits payments (Social Security, VA, retirement, etc.), Treasury regulations prohibit banks from knowingly accepting direct deposit payments for a person who is not an owner of the account receiving the payment. And permitting any non-customer to have any form of direct deposit made to a customer's account would create a situation in which the the bank would be providing banking services to someone who has not been "cleared" using the bank's CIP procedures, a potential violation under BSA/AML regulations.