The issue of hemi- and homonyms is an unsolved topic in the Big Data era, where informatics and technicians, rather than biologists or taxonomists, analyze huge datasets. Nowadays, taxonomic nomenclature is ruled by four independent international codes, and according to them, the existence of hemihomonyms and homonyms is accepted under some conditions as an exception to the general rule. This situation entails confusion, disagreements, and a plethora of problems whose consequences could worsen in the near future within the framework of the big data era. Moreover, the increasing use of big databases and analyses, data science, bioinformatics, biological monitoring, and bioassessment has shown such exceptions to be inconvenient, since these exceptions to homonyms are considered as duplicates by databases and statistical software, which are handled by non-taxonomist experts. International Codes of Nomenclature must change within the new context of big data analysis. This work aims to propose the elimination of any exception to the presence of homonyms and to evaluate whether the Independence Principle makes sense within this new context. Increasing coordination between several independent nomenclatural systems is essential and, perhaps, we must conduct our efforts towards a universal species list, finishing with the historical schism between Codes.