You can pronounce any Greek name now, no need to worry.
Easy way is to recognize the Greek name split it into however many syllables. 'E' endings have 'ee' sounds. Works for lots of the names mentioned on here
Eurydice - yoor-rid-dee-cee
Parthenope par-the-noh-pee
Antigone an - tig- oh- nee
Eirene - Eye-ree-nee
and so on.