11QMelchizedek

The text itself, 11Q13, Col.2.8, “when he shall atone for all sons of light and the people who are predestined to Melchizedek…upon them…For this is the time decreed for the year of Melchizedek’s favor, and for his hosts, together with the of the holy ones of God, for a kingdom of judgement, just as it is written concerning him in the songs of David, ‘A godlike being has has taken his place in the midst of the council of God; in the midst of the divine beings he holds judgment’ (Ps.82.1). Scripture also says about him, ‘Over it, take your seat in the highest heaven; a divine being will judge the peoples’ (Ps.7.7,-8).” Line 24-25 adds, “Your divine being is Melchizedek who will deliver them from the power of Belial” A related text, 4Q545, Frag.2, Col.3.15, “while I am Melchizedek…..from the height to the depths, I am ruler over all light” (Wise, Abegg and Cook, The Dead Sea Scrolls, 2nd ed., Harper, 2005). Another Psalm that may relate crucially to these texts is Ps.110.4, which is translated in most Bibles as something like, “Like Melchizedek, you are a priest forever”(NAB). However, consonantal ancient Hebrew is ambiguous in this verse. The JPS translates it, “You are a priest forever, a rightful king by my decree” The Jewish Study Bible, 2nd ed., notes here, “The translation…depends on whether ‘malki-tzedek’ is understood as two common nouns (a rightful king) or a personal name, ‘Melchizedek’” (who appears in Gen.14.18). Wise Abegg and Cook suggest yet another translation of Melchizedek, “ruler of righteousness”. James Kugel, in ‘The Bible As It Was’, discusses this verse in the context of the entire psalm, concluding that depending on how it is understood can make the “righteous king” the subject of the psalm, and thus it is he who sits at God’s right hand, dispensing justice, and generally taking care of business, and it is this interpretation that the DSS sectarians seem to have used for Melchizedek.
Check out Gard Granerød’s Abraham and Melchizedek: Scribal Activity of Second Temple Times in Genesis 14 and Psalm 110 (De Gruyter, 2010), he gives a full discussion on why there is probably no proper name in Psalm 110:4.