The Reverse ("back") of the coin was designed by Miley Frost (at the time, Miley Busiek). Hence the MB. The JW are the initials of the original engraver of that image. [BTW- the obverse ("front") of coin was designed by, Augustus Saint-Gauden].
The initials you have observed under the neck of Miss Liberty belong to the designer, Anthony de Francisci. See the Related Question for values.
they were equal as Eisenhower was commander in Europe and Macarthur was commander in the far east. however, eisenhower served under Macarthur years before WW2
secretary of state under president eisenhower, John Foster Dullis
Under the Eisenhower administration, US Military Advisers were sent to Vietnam in 1955.
They're the engraver's initials - Dennis R. Williams
On the reverse side of the coin under the DO in DOLLAR.
Look at the reverse for the phrase TRADE DOLLAR under the eagle.
If it has one it will be on the reverse under the eagle and above DO in the word dollar.
"F G" are the initials of the designer Frank Gasparro. His initials also appear on the back of the cent and half dollar, among other coins.
Mintmarks are on the reverse under the eagle.
The mint mark on a Morgan dollar (if any) will be found on the reverse of the coin under the wreath between the "D" and "O" in "DOLLAR".
The mintmark (if it has one) is on the reverse under the eagle.
If you are asking about a small (13mm) 1853 Liberty Head gold dollar, the mintmarks are on the reverse under the wreath.
The mint mark on a Barber Half Dollar is located on the reverse side right under the tail of the eagle.
The site under Related Links below has a number of very good images.
If it has one it's on the reverse, just under the eagles tail feathers.