The name Derek is a German baby name. In German the meaning of the name Derek is: Gifted ruler. From Theodoric. American Meaning: The name Derek is an American baby name. In American the meaning of the name Derek is: Gifted ruler.From Theodoric.n English the meaning of the name Derek is: Gifted ruler. People ruler.Old German TheodoricFamous bearer: Derrick was a 17th century hangman at Tyhurn, whose name became synonymous with 'gallows' and now refers to a type of crane.'Gifted ruler.' From Theodoric.