OP doesn't mean Iolanthe (although it is another nice Greek name). All three names they have listed are legitimate names in their own right.
OP, I think it's quite likely you'll get the eye-anthee pronunciation for Ianthe on occasion, so if that will bother you, it might be worth going with one of the other two. FWIW, I don't think eye-anthee is wrong, I think it's a variation, as it's in line with the English pronunciation of other Greek names borrowed into English like Iolanthe(!), Iris, Irene, and Sophia (originally pronounced suh-fye-uh here). But I do agree that ee-anthee is much nicer. I imagine you would end up having to correct the pronunciation of all the names at some point, though. Even Xanthe will probably get "Xanth" on occasion.