The current design is not very helpful for managing names for taxa with decent numbers of common names entered.
Can the design be change so that:
after the position 0 name which is the global default, names are sorted by language, so all the Spanish names are together, all the English names are together etc. Whether something is in position 4 or 14 is meaningless, what is relevant is the relative position within the language
possibly make the default global name a separate ‘box’ or place where it is positioned and can be changed