In Islamic tradition, during the Isra and Miraj (the Night Journey), Prophet Muhammad traveled from Mecca to the Al-Aqsa Mosque compound in Jerusalem. While the exact gate through which he entered the city walls is not named in the Quran, regional traditions often associate the northern access from the road to Damascus with the historical approaches into the Old City.
Jesus traveled repeatedly between Galilee (in the north) and Jerusalem. The route from Galilee enters Jerusalem directly through the northern side of the city wall, where the Damascus Gate stands today.
Coming from the Judean wilderness and the Jordan River region to the north and east, traditional accounts place his movements and preaching in the areas surrounding Jerusalem's northern and eastern entry points.
Though recognized as an apostle in Christianity rather than a prophet, Paul famously traveled from Jerusalem north toward Damascus to persecute early Christians before his conversion on the road to Damascus. The Damascus Gate gets its modern English name precisely because it marks the starting point of the ancient highway leading out of Jerusalem toward Damascus.