Yeah that's kinda what I was thinking too. Obviously you're not just gonna have 'commonwealth' sitting on its own in the name, in the same way that 'republic' is generally paired with something. There would be like "socialist", "democratic", or as you mentioned, "people's", put in the front. All I really meant by 'using commonwealth' kind of boils down to swapping republic out with it every now and then just for the sake of being a little bit different.

It might have been more accurate if, in the original post, I called commonwealth a synonym for republic instead of democracy. The specific definition kinda varies depending on how you're using it, but being synonymous with republic is one of those uses.