Elissa is used as a synonym for Dido in the Aeneid, and I imagine that this was because it fits more conveniently into the rhythms of Latin poetry. I don't know where Virgil got it from, but he doesn't come across as the kind of lad who'd invent names from scratch. Since the unfortunate Phoenicians lost several rounds in ancient historical times (against the Romans and the Israelites, not to mention the odd Egyptian, Persian etc) we don't have enough written texts to do proper research. So the best bet for a name meaning might be "widowed queen ditched by boyfriend for the loftiest of moral reasons"! And the safest bet for an origin might be "literature" rather than "mythology".