What does Nerida mean?
Associated with the Greek Nereids, the sea nymphs who were daughters of the sea-god Nereus, and with Greek neros 'water'. The name itself appears to be a relatively modern coinage (a popular Australian claim of an Aboriginal 'water lily' meaning is poorly documented), so treat the sea-nymph sense as its best-supported reading.
What does Ianthe mean?
From Greek 'ion' (violet) + 'anthos' (flower), giving 'violet flower'. Borne by a figure in Greek mythology (an Oceanid) and used by Lord Byron. A minority of sources offer alternative roots, but 'violet flower' is the standard etymology.