Ok, found the rule: A person's initials are a kind of abbreviation, and these are usually followed by full stops: John D. Rockefeller, C. Aubrey Smith, O. J. Simpson. Increasingly, however, there is a tendency to write such initials without full stops: John D Rockefeller, C Aubrey Smith, O J Simpson. And note the rare special case illustrated by Harry S Truman: the S in this name never takes a full stop, because it's not an abbreviation for anything; President Truman's parents actually gave him the middle name S. So that would mean that Mr. Morgan would have a middle name.
Found it: http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=robinp&id=I01566 •Name: George Thomas MORGAN •Sex: M •Birth: NOV 1845 in Birmingham, WAR, ENG 1 •Death: 4 JAN 1925 in Philadelphia 2 •Event: OCC Engraver •Event: DWEL 1890 4712 Chester Ave, Philadelphia 3 •Event: IDNO 27X •Reference Number: 1566 •Note: Won a scholarship to the Art College, South Kensington. Went to US Mint at Philadelphia to become engraver; designed "Head of Liberty" for 1878 and later silver dollars - the "Morgan Dollar"; Peter Brown said they were worth up to $750 in the 1960s; Lois[?] said the 1895 one was worth $8400[?] in 1978. He became Chief Engraver only in 1917, after most of his best work had been done.
Cool! I love a mystery solved! Thanks for finding the answer! ...and for confirming my guess for 'Thomas' in post #2
Great work mrh757! I've emailed the person who uploaded the information, hopefully they'll be able to provide the original document with his middle name, that would be really cool to see.