Pick up a newspaper today and you will read about activities of the Federal government, the same one that existed during the war. If you were in the National Guard and your unit was called up, you would be in Federal, not Union service.
Using the reasoning you set forth, military forces employed to surpress the colonial rebellion in America should be called Union because the represented the United Kingdom. I would like to get your reponse, but not on this board, please. "News and Views" is the proper forum.