Which statement regarding the classification of microorganisms is false? Bacteria contain internal membrane-bound organelles, which include ribosomes and inclusions. Cell morphology (shape) is not terribly useful when classifying bacteria, although it is useful in identifying bacteria. Every known living organism is assigned two names, a genus name and a species name. This system is called binomial nomenclature. All three domains (Bacteria, Archaea, and Eukarya) contain single-celled microorganisms. .