In a language like English, the distinction between "singular" and "plural" forms would be called a "grammatical feature" or "grammatical category". (This is a different use of the term "category" than in the OP.) The term is most frequently applied to "obligatory (grammatical) categories", i.e., to those that are present in every word within its word class. In English, nouns and some other word classes are always singular or plural, although in some cases there's no morphological or even semantic difference. A singular noun usually has its way of forming the corresponding plural form, but sometimes it doesn't.
The situation can be different in other languages. The grammatical category of "number" (i.e., singular vs. plural) can be non-obligatory (perhaps I should even say "non-existent", as a grammatical category). In those cases a noun can be typically used without such a grammatical distinction, while there's a semantic distinction which is however generally inferred from context. Sometimes the context is insufficient to determine whether the speaker is referring to a single member of a "category" (in the sense of the OP) or to many members of the category; and the language provides an optional lexical or grammatical mechanism that can disambiguate this when needed.
Word making generally consists not just in determining the form and the meaning of a new word, but also in setting some precedent as to how the new word will be used within the grammar of the target language (assigning values for grammatical categories, and possibly supplying the inflected forms). Different word making strategies seem to come with the respective conventions for where the new word ends up grammatically.
And so on.
The details of this are language dependent and academical grammars of inflected languages tend to include voluminous chapters on word formation.
However, if you take a language like Thai, there's no reason to dwell on whether a new word is singular or plural, because it is, in its base form, both - or neither, as you please. That's quite different from English. We'd say that the Thai noun is normally unmarked for number. It is possible to mark the number when constructing a sentence, but that's not the task for the maker of a new word.
I think that Mandarin and Thai are rather similar in this respect.