This Name Sounds Every Bit As Lovely As Its Meaning. Jessamine Is A French Girls Name That Means "jasmine," A Flower Used To Symbolize Love, Beauty, And Purity. It Also Has Persian Roots, Coming From The Word yâsamin for The Flower, Which Has Led To Names Like Yasmin And Yasmine. Jessamine Combines The Pep Of Jessica With The Elegance Of Jasmine, Resulting In A Baby Name As Striking As Your Little One Is Sure To Be.