The newly adopted International Code of Nomenclature for algae, fungi and plants (ICN) demands that dimorphic fungi, in particular those with both sexual and asexual names, now bear a single name. Although priority is no longer associated with the mode of reproduction, the ICN requires justification for choosing an asexual name over an existing sexual one. The phylogenetic approach that made dual nomenclature for fungi obsolete can be used to help choose names for large groups of fungi that are best known by asexual names. Here we apply this approach to one of the largest and most diverse asexual genera, the genus Aspergillus. We find that existing sexual names may be given to well supported clades of fungi with distinct phenotypes, which include sexual morphology as well as physiological attributes associated with xerophily, thermophily and mycotoxin production. One group of species important to food production and food safety, Aspergillus subgen. Circumdati, lacks a well supported clade; here we propose that the name Aspergillus be retained for this group. Recognizing that nomenclature has economic and social implications, particularly for old, important genera, we discuss the consequences of various scenarios to implement the new ''one name for one fungus'' article in the ICN, showing that our approach requires the fewest appeals to the ICN while retaining the name Aspergillus for many of the most economically and socially important species.