This song is in the DT (click here), but the lines are a bit jumbled, the racial references have been deleted, and there is no attribution. It may well be an accurate transcription of someone's recording, but it has been folk-processed a bit. Here is the original:

From The University of South Carolina Sheet Music Collection:

MY NAME IS MORGAN, BUT IT AIN'T J. P.
Words, Will A. Mahoney; music, Halsey K. Mohr; 1906.

1. A coon named William Morgan took his gal to see a play,
And on their journey homeward, they stopped in to a café.
As soon as she got seated, Liza grabbed the bill of fare,
Called the waiter, and she ordered ev'rything was there.
Bill says, "I knows you're hungry, gal, and I don't like to squeal,
But who do you suppose is gwine to pay for such a meal?
I'm satisfied to buy you two or three things that are there,
But the appetite you've got tonight would break a millionaire."

CHORUS 1: My name is Morgan but it ain't J. P.
There's no bank on Wall Street that belongs to me.
Forget your champagne appetite.
The best you'll get is beer tonight.
My name is Morgan but it ain't J. P.

2. Bill Morgan married Liza thinking he could change her way,
But what she did to William's purse I'm most ashamed to say.
Whenever she went shopping, she'd buy ev'rything she'd see,
And what she couldn't pay for, she'd have sent home C. O. D.
One day six big deliv'ry wagons backed up to Bill's door.
They asked him to accept the goods while they went back for more.
It didn't take Bill long to go and get his hat and coat.
When Liza came back home that night, she found this little note:

CHORUS 2: My name is Morgan but it ain't J. P.
You must think I own a railroad company.
You might know me pretty long,
But you've got my initials wrong.
My name is Morgan but it ain't J. P.

[Recorded under the title MORGAN AND HIS GAL by Don Cherry, Walter Smith and Friends, The New Lost City Ramblers, and Anne Hills & Cindy Mangsen. A version called MY NAME IS MORGAN was recorded by Chad Mitchell and by the Mitchell Trio. Max Morath recorded it as MY NAME IS MORGAN (BUT IT AIN'T J. P.).]