The identification of cortical sulci is key for understanding functional and structural development of the cortex. While large, consistent sulci (or primary/secondary sulci) receive significant attention in most studies, the exploration of smaller and more variable sulci (or putative tertiary sulci) remains relatively under-investigated. Despite its importance, automatic labeling of cortical sulci is challenging due to (1) the presence of substantial anatomical variability, (2) the relatively small size of the regions of interest (ROIs) compared to unlabeled regions, and (3) the scarcity of annotated labels. In this paper, we propose a novel end-to-end learning framework using a spherical convolutional neural network (CNN). Specifically, the proposed method learns to effectively warp geometric features in a direction that facilitates the labeling of sulci while mitigating the impact of anatomical variability. Moreover, we introduce a guided-attention mechanism that takes into account the extent of deformation induced by the learned warping. This extracts discriminative features that emphasize sulcal ROIs, while suppressing irrelevant information of unlabeled regions. In the experiments, we evaluate the proposed method on 8 sulci of the posterior medial cortex. Our method outperforms existing methods particularly in the putative tertiary sulci. The code is publicly available at https://github.com/Shape-Lab/DSPHARM-Net.