The name Salem in the Bible
Salem is the place where Melchizedek housed (Genesis 14:18). After the war of Four against Five Kings, Abraham's nephew Lot is abducted and Abraham sets out with a small army to rescue him. When they do, they loot the abductors while they're at it, and bring back the spoils. This evokes gratitude among the locals, among whom king Melchizedek of Salem.
Melchizedek achieves legendary status in the Bible, also because the town called Salem is renamed at some point, and becomes known as Jerusalem. According to Psalm 76:2 God's tabernacle is in Salem.
The name Salem appears twice but in only one passage in the Greek New Testament, and this in conjunction with Melchizedek (spelled Σαλημ; Hebrews 7:1-2).
Etymology of the name Salem
Originally the name Salem probably had to do with a Ugaritic god, but transliterated this name neatly concurs with the Hebrew verb שלם (shalem) meaning to be complete, sound, and the familiar noun שלום (shalom), meaning peace:
Most translators interpret the name Salem with Peace or At Peace (NOBSE Study Bible Name List, Jones' Dictionary of Old Testament Proper Names) but more accurate is Perfect or Complete.