Jamieson, Fausset and Brown on 2 Samuel 5:9

9. David dwelt in the fort, &c.--Having taken it by storm, he changed its name to "the city of David," to signify the importance of the conquest, and to perpetuate the memory of the event.

David built round about from Millo and inward--probably a row of stone bastions placed on the northern side of Mount Zion, and built by David to secure himself on that side from the Jebusites, who still lived in the lower part of the city. The house of Millo was perhaps the principal corner tower of that fortified wall.