Here are some possibilities on the Charles Miller.
Miller, Charles F. Company K, 1st Heavy Artillery. This company was from Shelby County.
Miller, Charles P. Company G, 21st Infantry Regiment. This company was from Shelby County.
Miller, C. Company K, 3rd Cavalry Regiment. This company was from Shelby County.
Here are some possibilities on John B. Miller.
Miller, John. 15th Infantry Regiment. Companies B, C, 1st F, 2nd F, H, I, and K were from Shelby County.
2 each Miller, John show up in Company K, 15th Infantry Regiment.
Miller, John B. Company K, 1st Heavy Artillery. This company was from Shelby County.
It looks like that there may be a correlation between the two that served in Company K, 1st Heavy Artillery, BUT, you would really have to research all the Compiled Service Records to rule out other possiblities.
I had no luck on Jens Heinrich Fredrich Bruun Neergaard. He does not show up for either Confederate or Federal service from Tennessee. I also looked at various variations of the name and still had no luck. HOWEVER, many Unionist Tennesseans did go to Kentucky and join up with Ohio and Kentucky units. Don't limit your scope to Tennessee units.
I hope this helps.
Gerald D. Hodge, Jr.
War Between the States Historian
Historian: 39th Georgia Volunteer Infantry Regiment