Parallel Anthology Track 14
Track 14: Kelly Harrell and the Virginia String Band - My Name is John Johanna Victor 21520-A; Recorded in Camden, New Jersey, 23.3.1927
The Roud Folksong Index classifies this song as a version of Roud 257. A Roud number search for this song  returns a number of records of versions collected prior to Harrell's recording, dating as early as 1906, and across a wide geographical area (Kentucky, N Carolina, Missouri, Virginia, W Virginia).
It seems likely that this composition is public domain, and there is no firm evidence to contradict this assumption as yet.