How to name substructures of a molecule using SMARTS patterns?

Question

[phoenix.sum13]

Does a standardized naming convention exist for molecular substructures, similar to how IUPAC assigns systematic names for entire molecules? I have a set of SMARTS patterns and want to assign meaningful names to them for easier grouping and organization. I attempted to use PubChem's substructure search, but it only lists molecules containing the substructures, not their specific names. How should I proceed to name and group these substructures systematically?

Thank you