Contrary to the traditional claim that needs for unambiguous communication about animal and plant species are best served by a single set of names ruled by international Codes, I suggest that a more diversified system is required, especially to cope with problems emerging from aggregation of biodiversity data in large databases. Departures from Linnaean nomenclature are sometimes intentional, but there are also other, less obvious but widespread forms of not Code-compliant grey nomenclature. A first problem is due to the circumstance (...) that the Codes are intended to rule over the way names are applied to species and other taxonomic units, whereas users of taxonomy need names to be applied to specimens. For different reasons, it is often impossible to refer a specimen with certainty to a named species, and in those cases an open nomenclature is employed. Second, molecular taxonomy leads to the discovery of clusters of gene sequence diversity not necessarily equivalent to the species recognized and named by taxonomists. Those clusters are mostly indicated with informal names or formulas that challenge comparison between different publications or databases. In several instances, it is not even clear if a formula refers to an individual voucher specimen, or is a provisional species name. The use of non-Linnaean names and formulas must be revised and strengthened by fixing standard formats for the different kinds of objects or hypotheses and providing permanent association of ‘grey names’ with standardized source information such as author and year. In the context of a broad-scope revisitation of aims and scope of scientific nomenclature, it may be worth rethinking if natural objects like plant galls and lichens, although other than the ‘single-entity’ objects traditionally covered by biological classifications, may nevertheless deserve taxonomic names. (shrink)