Bagrat - From Persian baga "god" and data "tribute", "gift" i.e. "god's gift". It is in use since ancient ages till now. We also have the surnames Bagratuni, Bagratyan.
Avakyan - is a name of Armenian origin. It derives from the Armenian word avag, meaning "oldest", perhaps signifying that a male ancestor was a prominent individual in his community. It may also mean "son of Avak".