The faith healer's name was Dr. James Rogers Newton, according to
Resa Willis, _Mark and Livy: The Love Story of MT and the Woman Who Almost
Tamed Him_ (New York: Atheneum, 1992), pp. 27-28. See also Willis'
article about Livy in the _MT Encyclopedia_ (New York: Garland, 1993), p.
156. Unfortunately I didn't spot an article about Newton. Willis (_Mark
and Livy_) cites vol. 2 of Paine's edition of _MT's Autobiography_, pp.
Incidentally, note that the "Christian Science" article in the _MT
Encyclopedia_ (not penned by Willis) seems to err in stating that it was
Twain's mother who was cured by Dr. Newton (p. 143).
Hope this helps!