Accurate brain parcellation in diffusion MRI (dMRI) space is essential for advanced neuroimaging analyses. However, most existing approaches rely on anatomical MRI for segmentation and inter-modality registration, a process that can introduce errors and limit the versatility of the technique. In this study, we present a novel deep learning-based framework for direct parcellation based on the Desikan-Killiany (DK) atlas using only diffusion MRI-derived data. Our method utilizes a hierarchical, two-stage segmentation network: the first stage performs coarse parcellation into broad brain regions, and the second stage refines the segmentation to delineate more detailed subregions within each coarse category. We conduct an extensive ablation study to evaluate various diffusion-derived parameter maps, identifying a top-performing combination of fractional anisotropy, trace, sphericity, and maximum eigenvalue that enhances parcellation accuracy compared with previously used parameter choices. When evaluated on the Human Connectome Project, our approach achieves higher Dice Similarity Coefficients compared to existing state-of-the-art methods. On the Consortium for Neuropsychiatric Phenomics dataset, where reliable voxel-wise DK reference labels in diffusion space are not available, our method demonstrates label-free evidence of robustness across different image resolutions and acquisition protocols by producing more homogeneous parcellations as measured by the relative standard deviation within regions. This work represents a step toward more practical dMRI-based brain parcellation by avoiding the need for anatomical MRI and subject-specific anatomical-to-diffusion registration at inference time. The implementation of our method is publicly available on https://github.com/xmindflow/DKParcellationdMRI.