Reportedly, after catching amateur games in the early 1880s he would tour St. Louis taverns, endlessly singing the song "Brennan on the Moor." Eventually, he became known as Brennan himself. The story is no doubt somewhat apocryphal, as is the version that he clandestinely assumed the identity of John Brennan, a boy who lived down the street from him, and to further baffle his pursuers he was listed for well over a century in baseball reference works as James Augustus Brennan, who proved to be a different man entirely. The first intimation that something odd was afoot with Brennan came when he and Perry Werden appeared in the TSN offices one day in the spring of 1890 and Werden informed TSN that Brennan's real name was John Gottleib Dorn, leading Brennan to counter that Werden was really Patrick Ward.
-Major League Baseball Profiles, 1871-1900, Volume 2
The entry on Brennan, which was written by Peter Morris and David Nemec, lists Brennan's actual name as John Gottleib Doering Jr., which is an even better name than John Gottlieb Dorn. It also mentions that Brennan, during the 1890s, worked winters at a gambling hall in Madison, Illinois, which is about thirty blocks from where I'm currently sitting.