I know of one region of the country where a single examiner says the bank must name the BSA officer in a separate resolution. He even insists that the BSA Officer must be reappointed annually. He will keep doing it until a bank realizes its just been accused of a pillar violation and says, "Bull..."
Look at how your bank names other officers and follow the same pattern with the BSA officer; e.g. if all officers are reappointed by the board each year include him or her on the list. However, if your policy makes it an ad hoc appointment, i.e. "The cashier shall serve as the BSA officer," then as long as you have a properly appointed cashier, you have a BSA officer.
If you are concerned that you heard the story about some examiners not accepting an ad hoc appointment locally, call the EIC from your last BSA exam and ask if it is an issue.
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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.