Cell types are fundamental biological units and partially independent evolutionary units, shaped by individualised gene regulatory networks and developmental lineages. Despite the recent explosion in single-cell sequencing and increased attention on cell characterization, we still lack a unified and consistent naming system for cell types that works across species. Since cell types are the products of evolutionary diversification, we propose that cell-type names should explicitly reflect evolutionary history, and suggest a naming system with a phylogenetic representation prefix as a simple, informative and intuitive way to do this. The key to this is establishing the evolutionary/taxonomic level of comparison, coupled with understanding homology and innovation in cell-type evolution. Put simply, it can apply to both individual cell types and their clades. We illustrate this approach using two case studies: chordate macroglia and more explicitly on vertebrate photoreceptors. The long-term goal is to stimulate progress towards a more coherent and informative language for cell-type identity and comparative analyses that is evolutionarily extendable as single-cell research proliferates across the tree of life.