Well historically modern greek is defined as the greek after 1453 so we are talking about modern greek in 1643
My apologies, I was thinking of some intermediate stage of Greek, good analogy mentioned by @Lascaris of Shakespearean's Early Modern English. However, regarding the actual terminology used, I think Apanemoi (Απανεμοι) would be the best literal translation but Ypínemes (Υπήνεμες) would still be more appropriate name for the islands (i.e. Leeward itself is not exactly a modern and commonly used English word but we still retain it for the name of a group of islands). A Google search reveals that there is more than double the amount of results for Απανεμοι but not one is actually related to the actual Leeward Islands compared to Υπήνεμες. But who knows, maybe the Romans decide to buck the trend and call it something else altogether.