Well, yeah, that is a little unreasonable to assume they would have a single account acting as both Personal and Business. Just like a bank account, you can only have one or the other. What types of transactions you run through an account of any type is up to you and your bookkeeping procedures. In general, it's not good to have both personal and business transactions going through a single account of any type. I think you need to focus more on the Facebook side. If you have people submitting payments to you through FB then it needs to be clear how they can do that correctly. You could setup specific links or buttons that are associated with the account you want people to be using, or link to a page of your own where somebody could choose a drop down like you're saying, and specify what they're paying for so that you can steer the money accordingly.
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