To bind oneself with a solemn oath — literally, to 'seven oneself' (from sheva, seven). In the ancient Near East, oaths sealed covenants, and seven was the number of completion/perfection.
God himself swears oaths (Gen 22:16; Heb 6:13) — the highest form of divine commitment, binding himself by his own name since there is no greater authority. Human oaths called on God as witness.
God's oath-swearing is unique: he binds himself by his own name because there is no higher authority. Hebrews 6:17-18 says God interposed with an oath so that 'we who have fled for refuge might have strong encouragement.'