John Pierpont Morgan (1837-1913), mortgage banker, was probably the most powerful financier in American history; he controlled railroads, steel mills and the largest bank on Wall Street. The size of his enterprises is demonstrated by the fact that his bank actually financed the Federal Reserve Board in its early years.
This was probably a vaudeville song. There is sheet music from 1906 published by Herbert H. Taylor, Inc, New York in the Baylor University Frances G. Spencer Collection of American Popular Sheet Music. It is subtitled "Coon Song". The first verse begins "A coon named William Morgan ..."
Sheet Music Cover

The first known recording of this song is by Bob Roberts, "My Name Is Morgan, But It Ain't J.P." (Edison 9227, 1906) I learned this from the New Lost City Ramblers, "Bill Morgan and his Gal" (on The New Lost City Ramblers Vol. 5).