Acoustic identification of individual animals (AIID) is closely related to audio-based species classification but requires a finer level of detail to distinguish between individual animals within the same species. In this work, we frame AIID as a hierarchical multi-label classification task and propose the use of hierarchy-aware loss functions to learn robust representations of individual identities that maintain the hierarchical relationships among species and taxa. Our results demonstrate that hierarchical embeddings not only enhance identification accuracy at the individual level but also at higher taxonomic levels, effectively preserving the hierarchical structure in the learned representations. By comparing our approach with non-hierarchical models, we highlight the advantage of enforcing this structure in the embedding space. Additionally, we extend the evaluation to the classification of novel individual classes, demonstrating the potential of our method in open-set classification scenarios.