My opinion is that Ivan is his evil alter-ego. He is him on the day of the accident, the sun glasses the boots , the clothes, everything.
He comes back and haunts him until he needs to finally admit his guilt. He doesn t exists in reality that s why the carpet is empty when he wants to throw the body, people at the shop don t know him, his acid quotes "You caused the accident..not ME"..or "What have I done with Nicholas?" meaning "why u blaming me...u were the one who killed him", the sign that he makes at the shop by showing cut throat with his thumb and then the work accident occur, the fact that he can drive his car on red light not bumping into the other vehicles..etc.
Also we can say Ivan is the Death itself because we see that he took Nicolas with him into car and enter both into building. He took him from the day of the accident and they are both on the other plan of existence. "C mon you know he is dead (speaking of Nicholas).He try to kill him without success, he reappears at the pier "Who are you?" and he finally recognize his guild and regain sleep and peace.
Also I think they put the name Ivan to this character regarding the legendary russian figure Ivan the Terrible who killed his own son and made a lot of murders, a sadist and a maniac. There is the motive of the one-hand thing also.
One hand on the wheel during the accident, Miller lose his hand, mill---Miller word asociation, one hand drawn on the refrigerator, one hand on the ride in the amusement park and the premonitory quote of Miller :" Reznik I need a HAND!" However the picture with Reynolds and him fishing explain everything. All sees him in the picture only he is the only who doesn t want to admit.
And if u look very closely and rewind movie u will see for few seconds in the scene where he chase Ivan s Pontiac firebird car he try to write down the plate numbers. 743 CRN or something...when he lose the car and gets down from his van you can see his plate numbers is the vice-versa of Ivan car 347 NRC.
That's another clue we can figure that Ivan is actually himself.And I think the director wanted to make analogy with the old Christian Bale American Psycho movie because this word appear few times, Stevie quote "My ex he s a fucking psycho" and when he throw him away from her home "you re a fucking psycho..fucking psycho..."
However is a great movie which needs to be seen few times to be fully understood and in different states of mind.