One of the essential tasks in connectomics is the morphology analysis of neurons and organelles like mitochondria to shed light on their biological properties. However, these biological objects often have tangled parts or complex branching patterns, which make it hard to abstract, categorize, and manipulate their morphology. In this paper, we develop a novel topological nomenclature system to name these objects like the appellation for chemical compounds to promote neuroscience analysis based on their skeletal structures. We first convert the volumetric representation into the topology-preserving reduced graph to untangle the objects. Next, we develop nomenclature rules for pyramidal neurons and mitochondria from the reduced graph and finally learn the feature embedding for shape manipulation. In ablation studies, we quantitatively show that graphs generated by our proposed method align with the perception of experts. On 3D shape retrieval and decomposition tasks, we qualitatively demonstrate that the encoded topological nomenclature features achieve better results than state-of-the-art shape descriptors. To advance neuroscience, we will release a 3D segmentation dataset of mitochondria and pyramidal neurons reconstructed from a 100μm cube electron microscopy volume with their reduced graph and topological nomenclature annotations. Code is publicly available at https://github.com/donglaiw/ibexHelper.