Albert Barnes Commentary Luke 1:59

"And it came to pass on the eighth day, that they came to circumcise the child; and they would have called him Zacharias, after the name of the father." — Luke 1:59 (ASV)

On the eighth day. This was the day on which it was required to circumcise children (Genesis 21:4).

And they called him Zacharias. The name of the child was commonly given at the time of the circumcision (Genesis 21:3–4). The name commonly given to the eldest son was that of the father.