Note
amyagThe word ամյակ is used for annual commemorations of events, a person's life milestone (e.g., a 90th "anniversary/birthday" celebration), or the founding of an organization.
So, while "ամյակ" can be a synonym for "birthday" in the sense of an annual celebration of one's birth, the more direct and common translations are ծննդյան օր or տարեդարձ.