In Hebrews chapter 7 the author writes about the life of the priest Melchizedek. Verse 3 of that same chapter tells us that Melchizedek is “Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually.”
How is it possible for Melchizedek to exist without parents? Through prior research I have read that Melchizedek may have be a king’s title, not a man’s name given, is this true?
To answer briefly, it is NOT possible for Melchizedek to have existed without having parents. That should be obvious. The intended meaning behind the Greek is that he had no genealogy or (recorded) parentage.
For this Melchizedek was ordained a priest after the order of the Son of God, which order was without father, without mother, without descent, having neither beginning of days, nor end of life. And all those who are ordained unto this priesthood are made like unto the Son of God, abiding a priest continually.
– JST Hebrews 7:3
The implication is that he wasn’t a priest of the Most High God because of his parentage or because he was born of a certain tribe like the Levites. He was a priest because of who he was in relation to God. He was a righteous man who was called directly to be His high priest. There was no earthly inheritance from which he derived his divine authority. But it was given him directly from God, Himself.
To answer your other question about Melchizedek being a king’s title rather than a man’s name is mostly true. But it is kind of like saying “The Great Emancipator” is simply a title for Abraham Lincoln. People who were not aware of who Melchizedek really was (such as the entire sectarian community) would obviously assume it was a mask someone wore. It could simply be a mantle that was passed down to many people. Melchizedek was the one for whom the high priesthood is named to avoid the too frequent repetition of the name of the Lord. And that particular person (whom we as Latter-day Saints assume was Shem) was indeed known as “A Great High Priest” to whom Abraham gave his tithes and offerings.