Why is Cuba called the "Republic of Cuba", while it is a Communist one-party state?

No, it is not a republic. But countries can call themselves whatever they want to. Who can stop them? It's just a PR move, so they can pretend they're following the will of the people.

No, not really. But then again, Communist China calls itself the Peoples Republic of China. North Korea calls itself the Democratic Peoples Republic.

Why is the US called United States?. I don't see it united at all.

check the dictionary.