Luke 1:60

And his mother answered and said, Not so; but he shall be called John.

This indicates that Zacharias had already informed Elizabeth of the name bestowed by the angel Gabriel. Of course, this, like all other communications from Zacharias during that period, would have been through written communication. Someone has remarked that Zacharias was "a quiet father" prior to John's birth!

The officiousness of the neighbors is seen in their appealing over the mother's wishes to Zacharias himself.