According to "Kojikiden" (Commentaries on the Kojiki) written by Norinaga MOTOORI in 1798, the part 'izana' came from the Japanese word 'izanau((meaning "invite") and the remaining 'gi' means a male.
「いざな」は「誘う（いざなう）」の語根で、「ぎ」は男性を表す語（本居宣長『古事記伝』1798年）。