Easy Fix?
Is there any legitimate reason for anonymous bank accounts other than fraud or tax evasion?
If so then perhaps some system of escrow where the identity is held secure unless there is fraud on the account.
If not then making sure all holders of bank accounts are traceable would pretty much stop this sort of fraud overnight - also make the banks liable for any losses fraudulently credited to an account where they can't locate the holder of that account.
In reality pretty much all bank mediated fraud could be stopped if the banks were liable for all losses, but at the moment there is no incentive as the banks profit from money moving about regardless of the legal status of that money.