Ben - From my AIB Law & Banking text: Owners of LLCs are called members. Members often operate the LLC themselves, or they may delegate that responsibility to managers...
...State law dictates the formation of an LLC...an LLC is created by filing articles with the state. Often an LLC will have an operating agreement...that sets forth how its business will be conducted.
So, if I'm understanding this correctly, A-B is the customer, but A-B-C-D is the "person" opening the account. If A-B is registered with the state (has a legal identity)and can furnish ID, then it is the customer. If A-B does not have a formal legal identity, then A-B-C-D is the one to CIP, but I would be very surprised (and cautious) if the latter were the case.