Whether or not your bank checks payee names when it's asked to help customers fill out PMOs will be a matter of bank policy driven by its OFAC risk analysis for the service/product. Clearly you can't check names if you aren't given them, however.
Do be aware that most states consider personal money orders a form of single-use checking account. As such, PMOs will be subject to stop payment orders.
You should also encourage customers to complete the PMOs before leaving the office, to protect themselves from loss.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8