Looking at all the previous answers it seems clear that you can only achieve the things you require, instant naming and single individual IDs (no accessing my facebook or bank account) if you invent a new measurable universal property that is unique to each universe.
Using my hand-held and waveable quantum signature gizmo I can measure each universes paralleism state. This is a simple guid, that the pocket device turns into a naming phrase, like what3Words, but auto generated from the GUID rather than relying on a hand cranked list.
You're still going to run out, over all your parallel universes quite quickly. But you should have enough locally unique names that your characters can't realistically travel far enough to meet a duplicate name.
On duplication, everyone used to live in CorrectHorseBatteryStaple, and now the duplicates live in SpaceBannanaBurningHole. It's annoying that I've become the B universe, but given the quantum signature doesn't change after duplication I've no choice but to believe the device.
How you get the two factor authentication to check my quantum signature is a puzzle I leave up to the bank. But obviously they don't have to actually care what the universe's signature is, just that the person accessing as the same one. So the bank's end could be plugged into, say, a small piece of fairy cake.