The robustness of Peer-to-Peer (P2P) networks, in particular of DHT-based overlay networks, suffers significantly when a Sybil attack is performed. We tackle the issue of Sybil attacks from two sides. First, we clarify, analyze, and classify the P2P identifier assignment process. By clearly separating network participants from network nodes, two challenges of P2P networks under a Sybil attack become obvious: i) stability over time, and ii) identity differentiation. Second, as a starting point for a quantitative analysis of time-stability of P2P networks under Sybil attacks and under some assumptions with respect to identity differentiation, we propose an identity registration procedure called self-registration that makes use of the inherent distribution mechanisms of a P2P network.