Dennis, I believe that the surname should also be shown as Ahearn (or Ahern), as Aheam is a rather uncommon surname. I believe that it would have almost certainly been an error in transcription on the part of those transcribing the names from the muster rolls or other handwritten documents of the time.
Although his surname is listed in the Medal of Honor volume as Aheam, his surname, in the ORN, series 1, volume 3, page 68, is shown as Ahern.
The volume, GENERAL ORDERS AND CIRCULARS, NAVY DEPARTMENT, 1863-1887, also shows his surname, on page 24, as Aheam (General Order No. 45).
The MOH volume indicates that he had enlisted aboard the USS KEARSARGE at France. His MOH citation reads, in part: "Carrying out his duties courageously, PmS. Aheam exhibited marked coolness and good conduct and was highly recommended by his divisional officer for gallantry under enemy fire."
It should be noted that in the heat of battle, every man was expected to do his duty, including those normally employed as clerks, or other non-combat duties. They would have had to assist the fighting men of the vessel in one way or another, and Aheam/Ahearn was no exception.