I vote Scandinavia for the civilisation (who needs Finland and Iceland anyway?) and Copenhagen for the capital (since it is the best well known). Cnut the Great should be at least one of the leaderheads since he is the most well-known leader of medieval Scandinavia. My second vote would be for Danes and Copenhagen. Norsemen gets too confusing with Norwegians in English and I don't think it would be well understood. If two mods were created, I'd vote for Danes and Swedes, but if there is only one civ, Scandinavia seems the most appropriate, even if the two states were only ever in a dynastic union (Kalmer) and never formally united.
Regarding the debate about various other states throughout history that Civ IV shafts, I agree that England is an improper name for the country and propose renaming it Great Britain, by which Scotland and Wales are no longer neglected (since both were independent during the larger portion of 4000 BC - AD 2050). At the same time, it would retain a legal name for the current state of the United Kingdom of Great Britain and Northern Ireland and actually match the first name the united country had between 1707 and 1800. Great Britain should not get a settler on Calais since Calais was not founded by the English rather by the Romans, Flemish, and Burgundians. Its part of the English empire was rather short-lived (c. 1066 - c. 1550).
China is a different matter. While China has at various points since pre-historic times been divided governmentally, I believe that it overwhelmingly has remained a culturally unified entity since at least the founding of the imperial state c. 250 BC. The only exceptions were during the Mongol and the various invasions, but none of those undid the cultural integrity of the Chinese state. The Han people have been a culturally united state since at least 250 BC.
Russia is certainly a different matter than either of the two above states. It has only been unified in some official capacity since the 1500s and prior to that was basically the target of Mongol, Hun, etc., animosity. Russia, of course, refers to White Russia, the western portion that has historically considered itself European rather than Asian or Middle Eastern. I think if it were to change names, Muscovy would be the most appropriate since that includes much of the era of Mongol occupation and links it back to the Kievan Rus days (although calling it the Keivan Rus would therefore also work). Ultimately though, where China is justified by a civilisation because of its cultural integrity, Russia, like Great Britain, should probably be retained as Russia, focusing specifically on its geographic origin and position. Any other name to call the state would probably confuse people and would not be any more appropriate than calling it just Russia.