John Lightfoot on Luke 1:59

[And they called it, &c.] I. "The circumciser said, 'Blessed be the Lord our God, who hath sanctified us by his precepts, and hath given us the law of circumcision.'" The father of the infant said, "Who hath sanctified us by his precepts, and hath commanded us to enter the child into the covenant of Abraham our father." But where was Zacharias' tongue for this service?

II. God at the same time instituted circumcision, and changed the names of Abram and Sarah: hence the custom of giving names to their children at the time of their circumcision.

III. Amongst the several accounts why this or that name was given to the sons, this was one that chiefly obtained, viz. for the honour of some person whom they esteemed they gave the child his name: which seems to have guided them in this case here, when Zacharias himself, being dumb, could not make his mind known to them. Mahli the son of Mushi hath the name of Mahli given him, who was his uncle, the brother of Mushi his father, 1 Chronicles 23:21,23.

"R. Nathan said, 'I once went to the islands of the sea, and there came to me a woman, whose first-born had died by circumcision; so also her second son. She brought the third to me. I bade her wait a little, till the blood might assuage. She waited a little, and then circumcised him, and he lived: they called him, therefore, by my name, Nathan of Babylon.'" See also Jerusalem Jevamoth.

"There was a certain family at Jerusalem that were wont to die about the eighteenth year of their age: they made the matter known to R. Jochanan, Ben Zacchai, who said, 'Perhaps you are of Eli's lineage, concerning whom it is said, The increase of thine house shall die in the flower of their age. Go ye and be diligent in the study of the law, and ye shall live.' They went and gave diligent heed to the law, and lived. They called themselves, therefore, the family of Jochanan, after his name."

It is disputed in the same tract, whether the son begot by a brother's raising up seed to his brother should not be called after the name of him that is deceased: for instance, if one dies without a son, and his name be Joseph, or Jochanan, whether the son that is born to this man's brother, taking his brother's widow to wife, should not have the name after him that afirst had her, and be called 'Joseph,' or 'Jochanan.' Otherwise, indeed, it was very seldom that the son bore the name of the father, as is evident both in the Holy Scriptures and the Rabbinical writers. It cannot be denied but that sometimes this was done; but so very rarely, that we may easily believe the reason why the friends of Zacharias would have given the child his own name was merely, either because they could by no means learn what he himself designed to call him, or else in honour to him, however he lay under that divine stroke at present, as to be both deaf and dumb.