How did MacDuff become Weems (WEMYSS)

As an abbreviated explanation, the MacDuff's had no surname in the traditional way we view it today. When MacDuff slew MacBeth in the name of the Pretender to the Throne Malcolmb he was rewarded for this deed by an Earldom in the region of Fife. Fife was known for it's finger inlets and caves which in the Scottish vernacular were called Wemyss. MacDuff assumed the name MacDuff Earl of Wemyss as his title and name. When surnames became popular MacDuff was the given name and Wemyss was the Surname. From that time on descendents were known with the surname of Wemyss. After coming to America most of the Weems followed their ancestor Dr. James Weems spelling of the name. Dr. Weems father spelled his name Wemyss, but he  never lived in America.