The Medal of Honor is often erroneously referred to as the Congressional Medal of Honor. That was never the official title or name of the award. According to several sources, the reason for the reference to the award as the Congressional Medal of Honor is because it is presented by a senior official, usually the President of the United States, in the name of the Congress of the United States.
An act of Congress on Dec. 21, 1861, authorized the award of a Navy Medal of Honor as "an award to such petty officers, seamen, landsmen and Marines who most distinguished themselves by their gallantry in action and other seaman-like qualities during the Civil War." Note that the award was for Navy and Marine Corps enlisted. Congress acted to begin the process for a Medal of Honor for Army enlisted on Feb. 17, 1862, but President Abraham Lincoln did not sign the legislation until July 12, 1862.
On March 3, 1915, Congress and the President acted to allow officers of the Navy, Marine Corps and Coast Guard to receive the Medal of Honor.
In that initial Act of Congress and through today the medal is referred to as the "Medal of Honor."
The Medal of Honor Society was founded in 1946. At first, it was not known as the Congressional Medal of Honor Society. Then, President Dwight D. Eisenhower signed legislation sent to him by Congress chartering the Congressional Medal of Honor Society. That charter, according to the Medal of Honor Society Web site, was signed on Aug. 5, 1958. The name reflects the name of the chartered society and not the name of the medal.