Atrial fibrillation (AF) is the most prevalent sustained cardiac arrhythmia and often requires catheter ablation procedures guided by electroanatomical mapping systems. Despite technological advances, anatomical segmentation of left atrial structures for the study of these 3D maps remains a manual process that limits reproducibility, scalability, and clinical integration. This study presents a novel deep learning pipeline for the automatic segmentation of anatomical regions on left atrial surface meshes. Three architectural approaches were developed and evaluated: MedMeshCNN, an edge-based convolutional neural network; PointNetGAT, a new graph-based model integrating vertex coordinates and attention mechanisms to capture topological context; and a novel hybrid two-stage pipeline combining both models. The combined architecture achieved the best performance on a data set of 174 left atrial meshes, particularly in anatomically complex and adjacent regions such as the left atrial appendage and pulmonary veins. The model pipeline yielded a mean accuracy of 0.88, a mean Intersection over Union (IoU) of 0.78, and a mean Dice coefficient of 0.87. Post-processing techniques, including mesh registration and label smoothing, further improved boundary consistency. An ablation study confirmed the contribution of each module, showing that prior anatomical information and spatial alignment significantly enhance segmentation quality. These findings demonstrate the effectiveness of graph-based deep learning for anatomical mesh segmentation and establish a scalable framework for patient-specific modeling, with direct applications in digital twin generation and personalized AF therapy planning.