Doppelgängers are external parts of Silent Swan that have become individuals by doing negative prints of Numbered. Silent Swan consists of thousands of Souls, most of which are concentrated in the core (the swan statue) and some of which are external (the wolpertinger and doppelgängers). The doppelgängers are individual Souls belonging to Silent Swan that have split off and become beings that function as individuals by "stealing" personality/looks/powers/etc from Numbered and merging with that, and they thus consist of two parts: The Silent Swan part and the Numbered part.

NOW. Once the invasion happens, the Silent Swan part will take over insofar as they will see only one goal: Defend Earth, and specifically the Neuschwanstein echo boundary, at all cost. What the rest of their personality does with that goal is up to the players.