1 Chronicles 11:3-7

So all the elders of Israel came to the king at Hebron, and David made a covenant with them in Hebron before the Lord; and they anointed David king over Israel, in accordance with the word of the Lord through Samuel. Jerusalem Is the Capital City

Then David and all Israel went to Jerusalem (that is, Jebus); and the Jebusites, the inhabitants of the land, were there.

The inhabitants of Jebus said to David, “You shall not enter here.” Nevertheless David took the mountain stronghold of Zion (that is, the city of David).

Now David had said, “Whoever is first to kill a Jebusite shall be chief and commander.” Joab the son of Zeruiah went up first, so he became chief.

Then David lived in the stronghold; therefore it was called the city of David.