NPS CWS&SS shows:

Soldier Name Side Function Regiment Name

Reed, Albert
Union Cavalry 2nd Regiment, Michigan Cavalry

Reed, Albert
Union Infantry 7th Regiment, Michigan Infantry

Reed, Albert D.
Union Sharpshooters 1st Regiment, Michigan Sharpshooters

Reed, Albert F.
Union Infantry 8th Regiment, Michigan Infantry

Reed, Albert H.
Union Infantry 24th Regiment, Michigan Infantry

Reed, Albert M.
Union Infantry 8th Regiment, Michigan Infantry

Reed, Albert S.
Union Sharpshooters 1st Regiment, Michigan Sharpshooters

Maybe you could narrow it down.