Melissa was the daughter of Melissus, king of Crete, and the sister of Amalthea. She is said to have been the first person to find a way of collecting honey, so is named from the Greek for 'bee' and also 'honey' itself, melissa.
We are told that she fed the infant Zeus with honey. Her name can be compared with that of Deborah, her Hebrew equivalent, since this also means 'bee'. Both names (especially the latter) have become fashionable as modern girls' names.