The name is John J. Davis. The letters "I" and "J" in 19th century cursive are hard to distinguish sometimes, so the occasional transcription error crops up from time to time.
Also, the age shown in Civil War military records are not always accurate.
John J. Davis, who served in Hawthorn's Arkansas regiment, and later in the 4th Arkansas U.S. Volunteer Cavalry, was described in the descriptive roll of the Union regiment as a farmer, age 22 (in 1864), born in McMinn County, Tennessee, eyes hazel, hair dark, complexion fair, height 5'10". There is no other John J. Davis or J. J. Davis from that part of the State who served in an Arkansas regiment.
Incidentally, this same John J. Davis first enlisted in Co. D, 15th (Northwest) Arkansas Infantry, at Dardanelle, Arkansas, on June 15, 1861; was mustered into Confederate service at Bentonville, Arkansas, on July 13, 1861; was wounded at Pea Ridge, Arkansas, on March 7, 1862; and was left behind to recuperate when his regiment was ordered east of the Mississippi River in April 1862. He never rejoined his regiment, but hooked up with Hawthorn's Regiment in July 1862.
When John J. Davis served in this regiment, it wasn't designated as the 15th (Northwest) Arkansas (though that's where the Compiled Service Records have filed his record). It was initially designated as the 3rd Battalion Arkansas Infantry, then the 21st Regiment Arkansas Infantry (not to be confused with another regiment with the same designation), and finally the 15th (Northwest) Arkansas Infantry (long after Davis had left the regiment) -- welcome to the wonderful world of Arkansas regimental designations!