I believe that Thomas J. Kennedy and T. J. Kennedy were one in the same and now I am trying to prove it.
T.J. Kennedy married Lucy Lauderdale on 7 Jul 1870 in Gallatin, Sumner, Tennessee
https://www.familysearch.org/search/records/index#count=20&query=%2Bgivenname%3ALucy~%20%2Bsurname%3ALauderdale~%20%2Bspouse_givenname%3AThomas~%20%2Bspouse_surname%3AKennedy~
I also have seen the posting for the Head Family cemetery on FIndagrave and have found a small obit in the 7 Sep 1876 edition of the Mephis Daily Appeal; page 4 that reads the following:"Dr. Thomas J. Kennedy, who served as surgeon in General Bates original regiment, died at his home last week in Sumner County, Tennessee"
Hope this helps!
Trevor