Who cares what Avon ladies do (no offense to any) - you're dealing with his situation and you're not comfortable with it- for good reason.
Obviously there are no regs that specifically tell you can't do as he is requesting, but to ensure that everyone is on the same page - are they ready to accept checks payable to another company into an account and run the risk of return for forged endorsement down the road for someone that they don't know?
As a brand new customer you have no history or understanding of what he's doing - stick to your guns - besides as many as I spent in the teller line I seem to remember Avon checks were always made payable to Mary Smith with Avon in the memo section - whatever.
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My comments are absolutely no reflection of, nor influenced by, my employer - take them at your own risk.