A Confederation if the parties involved still retain a high level of independency, or a Federal State if the most important powers have been transferred to the central Government.
The name for it is Empire.
Old Kingdom ~ i know ~
nation
Empire
A government ruled by a small group of people is an oligarchy.
empire
a manor
titan
A group of different peoples that are ruled by one ruler or by one government can be called many things. Ancient Rome ruled over such a diverse groups of peoples and ancient Rome is called an empire. This was the case with Great Britain until the end of WW 2. India, various island nations and such, like Ireland were all part of the British empire. In other situations a group of diverse peoples are in a nation and are ruled by a government. A case can be made that the US government rules a large number of different peoples. Most of the time, however, that term is not used.
A kindom.
empire
a group of nations ruled by a single person or government