Anatomical airway labeling is crucial for precisely identifying airways displaying symptoms such as constriction, increased wall thickness, and modifed branching patterns, facilitating the diagnosis and treatment of pulmonary ailments. This study introduces an innovative airway labeling methodology, BranchLabelNet, which accounts for the fractal nature of airways and inherent hierarchical branch nomenclature. In developing this methodology, branch-related parameters, including position vectors, generation levels, branch lengths, areas, perimeters, and more, are extracted from a dataset of 1000 chest computed tomography (CT) images. To efectively manage this intricate branch data, we employ an n-ary tree structure that captures the complicated relationships within the airway tree. Subsequently, we employ a divide-and-group deep learning approach for multi-label classifcation, streamlining the anatomical airway branch labeling process. Additionally, we address the challenge of class imbalance in the dataset by incorporating the Tomek Links algorithm to maintain model reliability and accuracy. Our proposed airway labeling method provides robust branch designations and achieves an impressive average classifcation accuracy of 95.94% across fvefold cross-validation. This approach is adaptable for addressing similar complexities in general multi-label classifcation problems within biomedical systems.