Meaning of Asha. Indian name. In Indian, the name Asha means-Hope.. Other origins for the name Asha include-Indian, Arabian.The name Asha is most often used as a girl name or female name.Indian Name Meaning-Hope.Origin-Indian.ther origins for the name Asha include-Indian, Arabian.The name Asha is most often used as a girl name or female name. Indian Name Meaning-Hope.