Hi HoHun.
The matter is very similar to the Bf/Me querelle. The official designation should be C. 202, as, like you stated, the M.C. designation was used only when the manufacturer's name was not spelled out.
Anyway, soon in official documents, both from the factory and the Regia Aeronautica, the two designations began to be used both, without particular care in choosing the one or the other.
So, while it's more correct to refer to Macchi planes as C. 20X, the M.C. form can be used, too.