The honor of being a Green Beret was not recognized until John F. Kennedy acknowledged their distinction in the U.S. Special Forces in 1962. The idea came from Special Forces’ founder Col. Aaron Bank where they were called “the unit with the greatest combat potential in the armed forces” in the 10th Special Forces yearbook from the time in the OSS. The green color was inspired during the World War II British Commando-type beret that was adopted by the Commandos in 1942. Up to this day, the beret had become a “symbol of excellence, a badge of courage, a mark of distinction in the fight for freedom.”
Source: https://www.armytimes.com/off-duty/2020/07/14/how-the-green-berets-got-their-name/