From Irish O'Sluaghain, for O'Sluaghadain, 'descendant of Sluaghadan', probably a variant of O'Sluaghadhaigh, from the Middle Ireland personal name Sluagadach, 'leader of a military expedition'.
 

Sluagadach, 'leader of a military expedition', appears as Slogadadh,
a leader of the Bishop of St Andrew's host, circa 1128.
 

An earlier Sluagadach went forth to Rome, circa 966 - 971.

(Black's 'Surnames of Scotland')