Don't miss Bessie's series at Ancestral Ties about John Morgan and Joseph Standing's mission travels:
The first linked post also contains links to her other posts about the two men.
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Additional note: John Morgan didn't ever seem to go by the name "John Hamilton Morgan" or "John H. Morgan." I have only looked at about a dozen vital records, but one of the first pages of The Life and Ministry of John Morgan notes that he may have been christened as "John Hamilton Morgan." No proof is given, though, so I am considering switching over the labels on my posts about John Morgan to reflect the name he used throughout his life.
However, the "Hamilton" name can be useful in distinguishing him from thousands of other John Morgans, as in the case of his Wikipedia article, so I'm really of a mixed mind about this.
A similar case of a similar era involves the Apostle Erastus Snow. After his death, some people started calling him Erastus Fairbanks Snow since he seems to have been named after Erastus Fairbanks, but his family has been making an effort in recent years to stamp out the use of the extra middle name.
Another case involves George Jarvis. At some point many years after his death, someone called him "George Franklin Jarvis" somewhere and the use of the false middle name spread like wildfire. I'm still trying to put that one out. Here's the post I've written about it. [Did George Jarvis Have a Middle Name? No.] My dad put a link to the post in George's FamilySearch Family Tree entry, and so far no one has tried to change his name back.
Theoretically I could give John Morgan the same treatment, but there are too many more pressing items on my to-do list, so I'll just have to raise the question here and then leave it.