In grammar we have singular and plural nouns. Is there one word to describe this component, like we have the word "tense" to describe the state of being "past", "present", or "future?" e.g.,

Whether the verb should be singular or plural depends on its [word-goes-here].

Number

See the Wikipedia article, for example.

For example, a linguist might say that the verbs in a language "agree in number" with their subjects.