This mysterious being is first mentioned during The Golden Chalice quest. A former high priest of Hyath claims him responsible for trapping the souls of those who died in the Temple of Hyath to remain there as undead.
The Church of the Sun Lord denies the existence of the Nameless One and considers those who believe in him blasphemers.
Spoiler: There are clues which can be interpeted as mentioning the Nameless One in various places during the story.
The "dark entity, whose name must not be called" is mentioned in Jachan's Diary found in Cult Site during Part 2. The diary describes the entity as being "nameless entity about death and undeath", and reveales that such entity was worshiped in the temple in the Cult Site at some time.
A clue to the involvement of the Nameless One in the history of the Isle of Prisoners can be found in the tale of Castle cleric's shadow. He tells about dead turning into undead as result of "influence of a terrible force". This phenomena is very similar to the one, seen in the Temple of Hyath, and attributed to the Nameless One. The portal which leads from Isle of Prisoners to the Cult Site, which according to Jachan's Diary served as the temple of "nameless entity", further deepens this connection.
In the Planes the Princess sees endless fields of tomstones. If she passes a Lore check, she remembers a book in which it was written about the realm of the Nameless One, filled with fields of tombstones.
The are some clues suggesting that the Old Man,whom the Princess meets in the Planes, is the Nameless One.
Trivia
"Nameless One" is the name of protagonist of Planetscape:Torment. Creature by this name is also mentioned in Baldur's Gate 2 in description of one of the items.
It is also the designation of the evil deity of "The Dark Eye", a german P&P RPG setting. Like in ADWR, the faith of the TDE nameless god practices demonology and necromancy, the god is "nameless" because his name must not be spoken, and it's often the greater evil that hides behind a cult of demon worshippers.