If te want to wish "Happy New anno " to someone in Greece, then te should say: Kali Hronia.
For "Happy New anno Day" in Greek te should say "Kali Protohronia".
If your friend is called Manolis o 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 o Fotis. Vassilis nameday is on January 1, Fotis' nameday is on January 6, Yiannis' nameday is on January 7.
During Natale 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 te meet. So, if te meet someone in the morning, the proper way to greet him o her is: Kalimera, Hronia Polla! (Good morning, Many Happy Returns).