Since the 51st Virginia represented part of the Confederate force at Fort Donelson, any reference to 51st Virginia by definition would have to be with this regiment. East of the Mississippi River there are no wartime examples of a state militia command being called into service and serving across a state line. Again, by definition, militia commands were specifically organized for state service.
The name confusion with the officer is understandable. A US War Department clerk may be to blame. However, IMHO almost any militia reference to a combat situation, especially a major campaign, should be immediately ruled out.