The Lich King's name in Wrath of the Lich King is Arthas Menethil. Once the crown prince of Lordaeron and a paladin of the Silver Hand, Arthas became the central villain of the expansion after merging with the Lich King at the Frozen Throne.
His fall began during the Scourge invasion of Lordaeron. Determined to stop the plague of undeath, Arthas made increasingly extreme decisions, including the purge of Stratholme. In Northrend, he claimed the cursed runeblade Frostmourne, which stole his soul and transformed him into a death knight.
Arthas later reached the Frozen Throne, defeated Illidan Stormrage, and donned the Helm of Domination. This fused him with the spirit of Ner'zhul, the original Lich King, but Arthas became the dominant figure. That is why Ner'zhul is sometimes mentioned in discussions of the Lich King's origins, while Arthas is the named antagonist players confront in Icecrown Citadel. After Arthas's defeat, Bolvar Fordragon took up the Helm to contain the Scourge.