Meaning of Jasmine. Persian name. In Persian, the name Jasmine means-a climbing vine plant that has fragrant flowers used to make perfume.. Other origins for the name Jasmine include-Persian, African.The name Jasmine is most often used as a girl name or female name.Persian Name Meaning-a climbing vine plant that has fragrant flowers used to make perfume.Origin-Persian.Alternate Origins-African.ther origins for the name Jasmine include-Persian, African.The name Jasmine is most often used as a girl name or female name. Persian Name Meaning-a climbing vine plant that has fragrant flowers used to make perfume. Origin-Persian. Alternate Origins-African.