Sweep accounts do generally tell you at which institution the deposits are being held, because it's critically important to know if you have an account there directly, as they'd both under the same FDIC coverage.
There aren't that many FDIC coverage categories. I'd guess that individual sweep accounts would end up in the revocable trust category, the same as most "regular" accounts? Or maybe sweep accounts would end up in the individual ownership category while regular accounts (with beneficiary) would be in revocable trust? This seems like the kind of question that by the time you'd benefit from knowing exactly (rather than just being overly conservative), you're paying professionals to manage all this for you. There's no need to make an amateur determination that you won't know is wrong until it's too late.
