Unless the recipient is not an established customer, the receiving bank's responsibilities for record retention are limited:
(iii) for each transmittal order that it accepts as a recipient's financial institution, a financial institution shall retain either the original or a microfilm, other copy, or electronic record of the transmittal order.
In essence, you keep what you received. There is no implication that you should reject the transaction or are responsible for extracting additional information from the sending institution.
Changing the subject somewhat, it has to be acknowledged that the record retention requirements for funds transfers do not stipulate that an "address" be a physical address. However, I suggest that originating banks require a physical address from the sender and send it along with the wire regardless of what the regulation says.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.