The answer depends on what country and which party of socialism and what level of leadership is being looked at.
Labor leader Eugene V. Debs and others formed the Socialist Party.
as a leader of Bulgarian Socialist Party
Before become leader of Fascist Party, Mussolini was associated to the Socialist Party.
He was the leader of the Nazi Party (National Socialist German Workers' Party) .
Eugene V. Debs
Hitler
The National Socialist German Workers Party
National Socialist German Workers Party
He was the leader of the National Socialist German Workers Party (Nazi Party).
July 29, 1921 was the day that the leaders of the National Socialist Workers Party acknowledged that Hitler had replaced Drexler (its founder) as leader of the party.
Nationalsozialistische Deutsche Arbeiterpartei or in English National Socialist German Workers' Party
Ben Salmon