Dust is Death's crow and his guide through his quest. He is commonly seen sitting on his master's shoulder. Dust serves a similar role to the Watcher in Darksiders, as Death's "clue giver". He may be summoned at any time, and will fly off Death's shoulder and caw at Death to point him in the direction he needs to go should he become lost.
Dust was given to Death by the Crowfather during a deal that they made, though he still shares a slight psychic link with his old master. Neither living nor dead, Dust is Death’s trusty sidekick. Dust will aid Death as he navigates the treacherous dungeons and explores the expansive overworld of Darksiders II. 
It is confirmed in the excerpt of the Abomination Vault novel that Dust was absconded from the Crowfather by Death, after their deal with the Nephilim amulet. The Horseman is very protective towards Dust, going as far as threatening angels in the White City itself and even Lilith with utter destruction if they dared to hurt the crow. Despite this, Death has shown to have little patience for Dust, particularly his attitude and especially when Dust hides during a fight.
His name is most likely a homage to the famous phrase "Ashes to ashes, dust to dust". From ashes life was born and to ashes life shall return and restart the cycle.