From the experts:
Jessamine, a charming name occasionally heard in England, is just beginning to be appreciated in the U.S. as a possible successor to all the Jess names of the past. It's also spelled Jessamyn, as in Quaker novelist Jessamyn West, author of Friendly Persuasion--who started life with Jessamyn as her middle name.
Jessamine began to be used as a first name in Britain around 1900, along with other flower-related names. Yasmin and Yasmine are other Jasmine variations.
This would make a great choice as a namesake honoring a Jessica.