If Ты want to wish "Happy New год " to someone in Greece, then Ты should say: Kali Hronia.
For "Happy New год Day" in Greek Ты should say "Kali Protohronia".
If your friend is called Manolis или Hristos, his nameday is on December 25 (Christmas day). Wish him "Hronia Polla" (Many Happy Returns) for his nameday.
The same applies if your friend is called Vassilis, Yiannis или Fotis. Vassilis nameday is on January 1, Fotis' nameday is on January 6, Yiannis' nameday is on January 7.
During Рождество holiday period, which lasts from December 24 until January 6, plus a couple of weeks past that, it is a custom in Greece to wish "Hronia Polla" to the people Ты meet. So, if Ты meet someone in the morning, the proper way to greet him или her is: Kalimera, Hronia Polla! (Good morning, Many Happy Returns).