Ambakum’s name day is December 2, the feast of Habakkuk the Prophet.
Churches that follow the Old (Julian) Calendar keep the same feast on December 15 of the civil calendar. See everything commemorated on December 2.
The saint behind the name

Habakkuk the Prophet
December 2, Prophet, Αββακούμ
The holy prophet Habakkuk is one of the twelve minor prophets of the Old Testament. Troubled by the prosperity of the wicked, he questioned God and stood upon his watch to await the answer, receiving the word that the righteous shall live by his faith. His prayer, the canticle beginning Lord, I have heard Thy report and was afraid, is sung in the Church as one of the biblical odes of matins.
Also celebrating on December 2
These names share the feast, many of them other forms of the same name:
What to say on a name day
The Greek wish is Χρόνια Πολλά (Chronia Polla), “many years.” A call or a short message on the day is what people remember. See name day wishes you can send and what a name day is.