Multiple realities
(covers information from several alternate timelines)

James, nicknamed "Jim", was the father of Winona Kirk and the maternal grandfather of George Samuel and James T. Kirk, the latter of whom was named after him.

In an alternate reality, James' son-in-law George suggested that his newborn son be named after James rather than his own father, his wife's choice. (Star Trek)

This character was only mentioned in dialogue.
According to the novel The Autobiography of James T. Kirk, his full name is James Ogaleesha Davis.