Zecharia Sitchin presents evidence that the Jerusalem of Palestine was a very ancient holy place/city. The massive foundation blocks are comparable to those of Baalbek in Syria and date to the "time of the gods".
My take is that this city was founded/dedicated to the god Ninurta-Geb, who had the epithet Me-salem/Mesilim. The Jebus people (Jebusites) who lived in this region could also have been named for Him, Jebus possibly being a local or Hebrew adaptation of the Egyptian name Geb.
But again there is the potential for confusion with this Jerusalem and the one at Thebes/Luxor in Egypt and perhaps even in other regions.
We have noticed this trend of establishing sister cities by the same name in the ancient world. Quoting from the third tutorial:
"Biblical Enoch is associated with the first city. Similarly, in myth Enki was associated with the world's first city, called Eridu of the underworld, and which perhaps was named for him by his father An. Likewise, Biblical Joseph is associated with Heliopolis (On/An), the primeval Egyptian city and a type of Eridu. Erech (Uruk/Unug) of Mesopotamia, site of the E-Anna temple, can also be considered as a type of Eridu, as can Jericho (Yerech-ow) of Canaan, the oldest continuously occupied city in the world."
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