Greek Meaning: 1  The name Terri is a Greek baby name. In Greek the meaning of the name Terri is: Reap; from Therasia. 2  The name Terri is an American baby name. In American the meaning of the name Terri is: Reap; from Therasia. 3  The name Terri is an English baby name. In English the meaning of the name Terri is: Abbreviation of Teresa, meaning harvester.