It looks to me that Cyprus is almost a bilingual country, with many signs in English, and some in Greek, according to a very quick search with Google street maps. Of course, you're the expert on this. My wild guess is that the mappers decided to choose one language, and the official language is presumably Greek, so that's what they used.
They may have no facility for translating names into another language. In this case it might be possible to transliterate names letter by letter (so 'ρ' -> 'r' always, and so on), but I have no idea how well that would work.
I would imagine that Cypriots would be familiar with both English and Greek alphabets; is that not the case? I'm assuming that most Cyprus names don't have a distinct English (anglicised) name.
Please pardon my ignorance of these things.