Does anyone know how John Morgan came to be called "John Hamilton Morgan"?

Group of Southern States Missionaries about 1880

3-John Morgan, 4-Matthias Foss Cowley (SS Mission 1880-1882)

Used with permission, John Hamilton Morgan Special Collections, Marriott Library, University of Utah, Salt Lake City, UT. purchased 2012.

Great Grandfather John Morgan's FamilySearch.org family tree is marked "Read Only." Amy's 2014 question is still found there and accessible.

Does anyone know how John Morgan came to be called "John Hamilton Morgan?" The book "The Life and Ministry of John Morgan," makes the following statement about the middle name, but the co-author, Nicholas G. Morgan Sr., does not give a source for the information: "Although christened 'John Hamilton Morgan,' the 'Hamilton' name coming from his mother's people, my father confined his name, throughout his mature life to 'John Morgan.'" Every record I recall seeing from John Morgan's lifetime calls him "John Morgan" with no middle name or initial, with the exception of the 1850 US Census, which calls him "John W." Anyone familiar with any letters or other sources that show him using the middle name "Hamilton" during his lifetime?
25 May 2014   by Amy Tanner Thiriot

During August of 1894 Matthias Cowley was attending to John Morgan as he lay dying in Preston, Idaho.  Cowley's journal entries reveal some helpful family history facts.

Last year cousin Karen discovered a drawer full of 5 x 7 index cards her Grandfather Nicholas G. Morgan had copied his own father's journal entries onto. Among the cards were eleven with Matthias Cowley's August 1894 journal entries.

The card I transcribed below is very telling.

(continued from the previous card where he is writing about Mary Ann Linton Morgan)

Aug 19 – 92 After moving away for some time, she again returned and again, the third time – and this time rented Adam Hunter’s house in which another little baby boy was born [Jan 26, 1894] and whom they called for me – Mathias Cowley. His father blessed him and I blessed him again the night after his father’s death.

After the burial, Mrs. Helen [lined through M. Morgan] Snyder and myself attended the services in the Tab. and listened to Pres. Housdale of the Michigan University on the Essentials of the Mind. After meeting called on Geo. A & Lucy Smith, his wife, the later a second cousin of mine. Returning to Bro. Morgan’s by request of Sis. Helen M. Morgan,  I blessed her little baby boy, sealing upon him the name of John Hamilton. Slept that night at Bro. Morgan’s.  

The following image shows three other index cards of the eleven in Nicholas Morgan's file drawer.

If there is interest, I will add the transcription of the other ten index cards that describe John Morgan's days at Preston, return train trip to Salt Lake and his funeral and burial.

Thank you cousin Karen.