The event that fixed his name is the killing of the Christians of Najran, an oasis in the north of his territory, in about 523. Two Syriac accounts carry it: a letter circulated by Simeon of Beth Arsham and the fuller narrative preserved as the Book of the Himyarites. Both were written by Christians, within living memory, for readers expected to be appalled, and both name Harith, the leader of the Najran community, among the dead. A martyr cult formed around him quickly and reached Greek, Ethiopic and Arabic literature.
The exegetical tradition of Islam connects the same episode with the people of the ditch in sura 85, though the Quranic passage names nobody and the identification is the work of later commentators rather than of the text. The two layers are worth keeping apart. That an Arabian king killed Christian subjects is attested outside the Islamic tradition; that a particular Quranic passage refers to it is an interpretation.
The end came within a year or two. Kaleb of Aksum crossed the Red Sea with a fleet, defeated the Himyari forces and installed a client regime. Himyar never recovered its independence, passing from Aksumite to Persian control before the Islamic conquests. How Dhu Nuwas died is not settled: the Arabic tradition has him ride his horse into the sea rather than be taken, which is the kind of ending a story acquires rather than the kind a chronicle records.