"But you, Bethlehem Ephrathah, Though you are little among the thousands of Judah, Yet out of you shall come forth to Me The One to be Ruler in Israel, Whose goings forth are from of old, From everlasting."
(Micah 5:2 NKJV)

Has not the Scripture said that the Christ comes from the seed of David and from the town of Bethlehem, where David was?"
(John 7:42 NKJV)

But thou, Bethlehem Ephratah,… But though Jerusalem should be besieged and taken, and the land of Judea laid waste, yet, before all this should be, the Messiah should be born in Bethlehem, of which this is a prophecy, as is evident from Matthrew 2:4.. The place is called by both the names it went by, to point it out the more distinctly, and with the greater certainty, Genesis 35:19; the former signifies "the house of bread", and a proper place for Christ to be born in, who is the bread of life; and it has the name of the latter from its fruitfulness, being a place of pasture, and as we find it was at the time of our Lord's birth. The shepherds were then watching over their flocks; and it is here added, to distinguish it from another Bethlehem in the tribe of Zebulun; from which tribe the Messiah was not to come, but from the tribe of Judah; and in which this Bethlehem was, and therefore called, by Matthew, Bethlehem in the land of Judah.

John Gill's Expository on the Whole Bible - Micah