Why was the single war between the Republic and The CIS called "The Clone Wars"?

Another possible in-universe answer is that the overarching Separatist Crisis, as well as the resultant Clone Wars themselves, incorporated a number of other concurrent wars/conflicts, such as the Summertime War, Sepan Civil War, Virgillian Civil War, Er'stacian clan war, Balith civil war, as well as earlier ones such as the Yinchorri Uprising, the Occupation of Karthakk and the Huk War.

These were mostly civil wars, but they could be seen as being contributory towards, and therefore later got folded into the description of, the overall war. For instance General Grievous emerged from the Huk War, and the Summertime War was a persistent conflict that was co-opted by the Clone Wars participants to become a proxy war.

Therefore, even though at the end of AOTC, when the formal conflict is just unfolding, Yoda refers to it as the Clone War singular, later on it may have been seen as a series of interconnected conflicts.