'...but the name of that city had been Luz previously’

‘…and he (Jacob) called the name of that place Bethel; but the name of that city had been Luz previously’  (Genesis 28:19)
On the left above is a fairly accurate depiction of the Mount Moriah complex as it would have appeared from the south and south-east before any structures or settlements there.
The blue line represents the stream of water flowing southward from the Gihon Spring in the Kidron Valley.
To the immediate left (west) of the spring and parallel to the stream is the ridge on which the City of David eventually stood. To the north the ridge tapers and then widens again to a bump on which today stands both the Mosque of Omar and the Shrine, the Dome of the Rock. In the view of many including this author, that bump is erroneously thought to be the site of Jerusalem's ancient temples.

The picture at left also reveals that the Mount Moriah complex as viewed from the high ground to the south would have appeared somewhat like a torso with shoulders, a neck and a head.
The name Luz means either almond or a bone of the neck (or even just neck).
In my view, as the site was developed with a settlement next to and around the Spring, the location became known as The Neck (Luz) and later as The Place (HaMakom) which I also believe is where Jacob had his dream and called the site Beit-El (Bethel or House of God).
 
Today the City of David area is completely covered with dwellings and buildings as shown in the picture at right which superimposes the area today over the ancient wall and the fortification which once protected the Gihon Spring.
 
In summary, the area around ancient Gihon became recognised and recognisable (depending on who was speaking and their background) by a number of different names; Salem, Luz, later Bethel then Jebus, Zion, the City of David and Jerusalem. (A modern Australian and simple example of a place with differing names would be the Aboriginal name Uluru which for many years was generally recognised by its European name, Ayers Rock. All over the world there are places known by differing names).
 
We are informed here in Genesis 28:19 that this site which Jacob named Beit-El (House of God), because of his dramatic encounter, was formerly known as Luz. 
It is entirely possible that this piece of land around the Gihon Spring and just to its north where this apparent Neck stood had become known by some as Luz for the reason stated above.
 
Read the story of 'THE PLACE HaMakom; where Jerusalem's temples stood' available here