The shape of the left atrium is a possibly critical biomarker for predicting the risk of atrial fibrillation. Traditional statistical shape analysis necessitates point correspondences across anatomical surface meshes, typically achieved by morphing a template mesh to a dataset of surface meshes using deformable registration techniques. While traditional optimization-based deformable registration methods yield excellent surface matching results, they are computationally intensive, hindering large-scale shape analysis. Furthermore, traditional deformable registration methods do not utilize multi-label surface meshes to guide the deformation process. In this study, we propose a novel learning-based multi-label deformable registration method for LA surface parameterization. Our method demonstrates surface matching results comparable to traditional methods, while maintaining the anatomical accuracy of the ostia of the pulmonary veins and the left atrial appendage, at considerably faster execution times.