There are only three popes in all of Church history who have earned the title “the Great” at the end of their names. And all three lived in the 1st millennium (unless you count St. John Paul II as a fourth).
St. Gregory the Great reigned from the end of the 6th century to the beginning of the 7th and is famous for his Pastoral Rule, he made some important liturgical reforms, and, of course, Gregorian Chant is named after him.
St. Nicholas the Great reigned in the 9th century and risked his life against the armies of the King of France to defend the indissolubility of marriage (read his amazing story here).
But the first pope to earn the title is St. Leo the Great, who reigned in the 5th century during the tumultuous years following the fall of Rome. He courageously fought heresy, defended the authority of the papacy, and personally defended the city of Rome from Attila the Hun’s approaching armies.