Jessamy \j(e)-ssa-my\ as a girl's name is a variant of Jasmine (Old French, Persian), and the meaning of Jessamy is "jasmine".
The baby name Jessamy sounds like Jessamae and Esmay. Other similar baby names are Jessamyn, Jessy, Jessey, Jessaka, Jessah, Jessaca, Jessa, Jessana and Sessame.