At his circumcision, the relatives wanted to name Elizabeth's baby after whom?

Answer: His father Zechariah

They were going to name him Zechariah after his father, but Elizabeth insisted, "He shall be called John."

“On the eighth day, when they came to circumcise the child, they were going to name him after his father Zechariah. But his mother replied, “No! He shall be called John.” They said to her, “There is no one among your relatives who bears this name.””— Luke 1:59-61 (BSB)