The Dead Sea is the English name, but not one of several by which it is known in Hebrew.
Genesis 14:3 gives it explicitly as the name of what was once Emek Ha Sidim (עמק השדים), but is now Yam ha-Melach, "the Salt Sea", in the plain of the five cities destroyed at the time of Lot. Can we deduce from this that there was once a valley there, but whatever happened to the Five Cities left behind a salt lake? And if yes, does that add weight to the speculation that what happened at Sedom was a massive volcanic eruption from deep beneath the earth?
See also Deuteronomy 3:17, which calls it "the Sea of Aravah, the Salt Sea - יָם הָעֲרָבָה יָם הַמֶּלַח", and, rather surprisingly, places it "tachat ashdot ha-Pisgah mizrachah - תַּחַת אַשְׁדֹּת הַפִּסְגָּה, מִזְרָחָה - under the slopes of Pisgah eastwards"; Pisgah being the mountain (properly the summit of the mountain, from pisgah = summit) where Moshe went to die (Deuteronomy 34:1). Which mountain? Most of what surrounds the Dead Sea is desert; on the western side there is that small hillock which King Herod once turned into a winter palace, and where the last Zealots of the Bar Kochba revolt committed mass suicide in 135 CE, and named Masada; the Dead Sea is certainly "eastwards" of this, but a hillock is not a mountain, and the top of Masada is a plateau, not a summit. Deuteronomy 34:1 tells us explicitly that "Then Moses went up from the plains of Mo-Av to Mount Nevo, to the top of Pisgah, which is opposite Yericho." This, however, is not east of the Dead Sea, but due north, so the text of Deuteronomy 3:17 is either in error, or referring to a different summit which does lie west of the Dead Sea, of which there is none.
Numbers 34:12 likewise names it Yam ha-Melach, the Salt Sea.
In Psalm 60:2 and 2 Samuel 8:13 it is given as Gey Melach (גיא מלח) = "the valley of salt". The region of the Dead Sea has one of the highest concentrations of salt in the world (only Salt Lake City in Utah can compete). In addition to the pillar of salt into which Lot's wife was apparently transformed (Genesis 19:26), the region abounds in what are called in Hebrew "Netsiv Melach" (נציו מלח), natural statues and columns made of fossilised salt. So important was salt to the Canaanite economy that it was even used in the making of covenants. A Brit Melach (ברית מלח) involving the eating of salt is mentioned in Numbers 18:19, 2 Chronicles 13:5, and referred to in Leviticus 2:13 as being also an essential ingredient of meat offerings. What exactly a Covenant of Salt involved is unclear. Jews today spill salt on their Sabbath challah, and claim because they need an explanation but don't have one that it makes the sweet bread slightly less pleasant, and this is a reminder of hard times suffered by Jews in days of yore; a slightly more literary answer than the traditional priestly evasion: "this is one of the divine mysteries that we are not meant to know". Salt is essential to remove the sacred blood from meat; but there is no need for salt on grain, and the texts that speak of the Covenant of Salt are specific about grain. Salt is a good preservative - is it intended as a "symbolic" preservation of the covenant? "Sharing salt" is a traditional Arabic expression of hospitality; could it be this? So many worthy suggestions, all of them findable in the links I have added here. There is even the hypothesis that Melach should read Malach, and that it is a Covenant with the Angel and not a Covenant of Salt at all; I shall not shame with a link to his article the otherwise distinguished Hebrew scholar who has made this suggestion, and who should know better than to mis-read Melach (מלח) for Malach (מַלְאָך).
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