The name Hazel is a Teutonic baby name. In Teutonic the meaning of the name Hazel is: Commander. The name Hazel is an American baby name. In American the meaning of the name Hazel is: Commander. The name Hazel is an English baby name. In English the meaning of the name Hazel is: The hazel tree;nut. A nut-bearing shrub; used since the 9th century, when flower and plant names became fashionable as first names.