In a recent essay on Christology, Paul Hoskisson offered the following commentary on Psa 110:1-4 and the origin of the term “Melchizedek Priesthood”:
The second point to be gleaned from a prosopological exegesis of Psalm 110 is that the Messiah was begotten before the creation of this world, thus more precisely identifying when the “begetting” took place. This point applies not only here but also in Psalm 2:7 (and this in Hebrews 1:5). There can be no question that in this prosopological reading, the Son of God became the Messiah before the beginning of the Creation narrative in Genesis 1 and was at that time, before mortal time was created, given the title Melchizedek, as verse 4 states.
The idea that Christ was begotten in an existence before this world was created is also not a new concept for Latter-day Saints, since the notion appears in Restoration scripture, particularly in the book of Abraham. But this is not the first time I have seen the Old Testament Psalms as a source for corroborating this doctrine. Additionally, this prosopological reading reveals that Psalm 110:1-4 is the only passage in LDS scripture that clearly states that Melchizedek is first and foremost Christ’s title that God the Father bestowed on Him in the pre-existence. In Hebrew, the title Melchizedek means “King of Righteousness,” an appropriate title for the Son of God and analogous to one of the titles for the Son found in Malachi 4:2: “Sun of righteousness.”
This understanding also undoes a Gordian knot that has interested me for years, namely, why the higher priesthood appeared to be named after a mortal—the man named Melchizedek in Genesis 14:18-20. The Doctrine and Covenants declares that the high priesthood is called the Melchizedek Priesthood “out of respect or reverence to the name of the Supreme Being,” that is “to avoid the too frequent repetition of his name, they, the church in ancient days, called that priesthood after Melchizedek, or the Melchizedek Priesthood” (D&C 107:4; see also verses 18, 73, and 76). Without the information contained in Psalm 110:1-4, it is easy to see why many Latter-day Saints assume that the higher priesthood is named after the mortal to whom Abraham paid tithes, though no scripture explicitly states that. In fact, Doctrine and Covenants 124 hints that the higher priesthood was not named after a mortal when it states that the higher priesthood “is after the order of Melchizedek, which is after the order of mine Only Begotten Son” (D&C 124:123). (Paul Y. Hoskisson, “A Plain and Precious Part Restored: An Essay Based on Matthew W. Bates’s The Birth of the Trinity: Jesus, God, and Spirit in the New Testament and Early Christian Interpretation of the Old Testament in BYU Studies 57/1(2018):181-97, here, pp. 194-95)
