Luke 1: 57-66, 80
God Has Shown Favor
In the events of the birth of John, most people recognize it as an act of God's "great mercy toward" Zechariah and Elizabeth. In fact, the name Zechariah that the neighbors and relatives want to give to the child is rather appropriate. It means, "Yahweh remembers." . They might have thought of the name when they considered the parents' old age and their lifelong faithfulness to God.  Their devotion to God's law is also indicated in this passage when Luke points out the fact that they have their son circumcised on the eighth day since his birth as prescribed in the law of Moses. 
However, they fail to see the extraordinary hands of God in it all. They cannot break away from the expected routine. "There is no one among your relatives who has this name," they argue with Elizabeth. With this sentiment, the name Zechariah, God remembers, could perhaps express a sense of entitlement. They live in the past. 
God does more for Zechariah and Elizabeth, for their newborn son, and in fact for the whole human race than just simply "remembering." Zechariah and Elizabeth have been told of God's favor by the angel (earlier in this same chapter, verses 11-17). Thus, in obedience to the angel, but also an act of faith, they name their son "John," the name means "Yahweh has shown favor"  or "God is gracious" . Zechariah and Elizabeth recognize God's favor and grace. They see the new day of God's salvation.
In Church today, we do not read Zechariah's prayer of praise that comes next in this chapter of Luke. But there, Zechariah praises, "Blessed be the Lord, the God of Israel, for he has visited and brought redemption to his people" (v. 68). It is no longer the past or the routine. It's now the new age of God's favor and redemption.
Zechariah and Elizabeth claim no entitlement with God. Rather, with the eyes of faith, they see God's graciousness in the events that others see as somewhat of routine, take it for granted, or even feel entitled to.
Do I see God's graciousness and favor in the ordinary events of my life and of the world surrounding me?
 Brian P. Stoffregen Exegetical Notes at CrossMarks Christian Resources, http://www.crossmarks.com/brian/luke1x57.htm
 Luke describes Zechariah and Elizabeth in these words, "Both were righteous in the eyes of God, observing all the commandments and ordinances of the Lord blamelessly. But they had no child, because Elizabeth was barren and both were advanced in years " (1:6-7)
 Genesis 17:7, New American Bible, Footnote