Read 2 Samuel 5:9 Using Other Translations
So David dwelt in the fort, and called it the city of David. And David built round about from Millo and inward.
And David lived in the stronghold and called it the city of David. And David built the city all around from the Millo inward.
So David made the fortress his home, and he called it the City of David. He extended the city, starting at the supporting terraces and working inward.