It was a common practice in the ancient Near East, as it is today, to rename a city when it comes into the control of a new group (see Numbers 32:41–42).1 The city had been captured by David; it now belonged to him and it was going to be his home in Israel going forward.
9 And David lived in the stronghold and called it the city of David. And David built the city all around from the Millo inward.