"签名登记离开" can be translated into English as "sign out after registration" or, in a more context-specific way depending on the scenario (e.g., in a workplace or hotel), "sign out upon completion of registration" or simply "sign out" (if the registration part is implied or already understood).
For a more concise and commonly used expression, especially in informal or day-to-day contexts, "sign out" is often sufficient, as it implies the process of formally indicating one's departure, which typically includes any necessary registration or acknowledgment steps.
If you want to emphasize the registration aspect more clearly, you could say "sign out after completing the registration process".