I should really stop trying to answer these kinds of posts so late at night haha.
Phoebe is spelled the same in Modern Greek (Φοίβη) and οι is pronounced as ee in Modern Greek. Phoebe is closer to FEE-vee in Modern Greek.
Yes, you're right, it is POY-beh (but with more of an H sound after the P sound, but not like F) in Classic Greek. Oh, I just found someone pronouncing it here:
http://www.forvo.com/word/%CF%86%CE%BF%CE%AF%CE%B2%CE%B7/
Anyway, I hope that helps.