This paper provides information on the origin and the etymology of the names of genera of Cyanophyta/Cyanobacteria in current use and on the way new names are formed under the provisions of the International Code of Botanical Nomenclature and the International Code of Nomenclature of Prokaryotes. Special emphasis is placed on the differences between the two Codes that should be taken into account when creating new names compatible both with the botanical and with the bacteriological nomenclature system, to support the ongoing efforts to harmonize the nomenclature of the Cyanophyta/Cyanobacteria under the two Codes.