Meaning of Daveigh. American name. In American, the name Daveigh means-beloved.The name Daveigh originated as an American name. The name Daveigh is most often used as a girl name or female name.American Name Meaning-beloved. Origin-America.n American, the name Daveigh means-beloved.The name Daveigh originated as an American name. The name Daveigh is most often used as a girl name or female name. American Name Meaning-beloved.