This article explores who designed the seal of the President:
According to the Encyclopedia of the American Presidency, the modern seal was first defined on October 25, 1945, by President Harry Truman in Executive Order 9646. It depicts an Eagle holding 13 arrows in one talon and an olive branch with 13 leaves in the other, surrounded by a ring of 50 stars (Executive Order 10860 added stars for Alaska and Hawaii in 1960) and the words “Seal of the President of the United States.” The words make it official. Otherwise, it’s considered the Presidential Coat-of-Arms; without the stars, it’s basically just the Great Seal of the United States, after which the Presidential Seal is modeled. The seal existed in various iterations before Truman –several can be seen embedded in the architecture and furnishings of the White House–but the 33rd President made a critical alteration to the design: he changed the direction the eagle faced. No longer was the symbolic representation of the United States looking toward the arrows or war, but to the olive branch of peace. Significantly, at the same time, the Department of Defense officially replaced the Department of War. According to Truman biographer David McCullough, the changes were intended to be seen as a symbolic of an nation both on the march yet still dedicated to peace.
The earliest seal was started by Millard Fillmore:
The earliest documented Presidential Seal was conceived by President Millard Fillmore in an 1850 sketch that he then sent to Edward Stabler, a nationally renown seal engraver. To say that Fillmore designed the seal would be a stretch – even to call his conception a “sketch” seems a bit generous. The heavy lifting was definitely done by Stabler....Stabler’s design appropriates the coat-of-arms first used on the obverse side of the Great Seal of the United States – whether or not that’s what Fillmore intended to communicate with his “eagle” sketch, we’ll never know. The Great Seal that inspired Stabler was first commissioned by a committee of our designer forefathers –Ben Franklin, Thomas Jefferson, and John Adams– during the Continental Congress on July 4, 1776.