The old man is found in the Volcano in the Planes. The Princess meets him following a nightmare during Chapter 6 - Dance with the Devil of the story and he is soon revealed to be a focal figure, playing a crucial role in the Princess's future. The old man proposes a deal to the The Princess, to steal statue from Delberg Castle in exchange for a lives of captive family members.
Spoiler: True identity of the old man is unknown, thou some suggest that there are clues that point out that he is the Nameless One. Those clues include:
Castle cleric's shadow suggests that some powerful influence lurking on the other side of the the breach turns all killed on Isle of Prisoners into undead, while a very similar phenomena which occurs in the Temple of Hyath, was accredited to the influence of the Nameless One.
The fact that Hyath serves or is somehow connected to the the Old man, further implies that the culprit of both stories is a same being.
Jachan's Diary mentiones that the Cult Site served previously as a temple for a "dark entity, whose name must not be called...nameless entity about death and undeath". The fact that the temple and the Isle of Prisoners were connected by a permanent portal and that the phenomena is about "death and undeath", further suggests connection between this "Nameless" entity and the "powerful influence lurking on the other side of the the breach".
A book the Princess remembers (if she passes Lore check) when seeing a tombstones in the Planes, in which it was written about the realm of the Nameless One filled with fields of tombstones.
The name of the journal entry describing the deal with the old man is a deal with the Devil.
Old Man has powers to ressurect dead people, even without their bodies, and to kill at whim, in resonance with description of the nameless entity mentioned in the Jachan's Diary as being about "death and undeath".
It may also be worth noting that he is always referred to as simply "Old Man", leaving him unnamed and thus being another allusion to him being the Nameless One.
There are however other opinions stating following counterpoints:
There is no evidence that the Old Man is responsible for the undead at all, it might just be the consequence of that kind of planar rift. Also there are no devils in the Temple of Hyath except Hyath if he is released from his captivity but there are in the Isle of Prisoners.
The fact Hyath serves the Old Man could just prove that the Old Man is a more powerful devil than Hyath. Also the way he infects Princess with Demon Pox by raping her suggests he is a sexual devil like Hyath and not the lord of the undead. Also robes are worn by male cultists of both Hyath and Balphagor but they are worn by the Old Man also and there are also strong paralells between the cults of both (robed men and naked women).
If Hyath serves this Nameless One, who rules over death and undeath then how does it fit with him being a 'god' of the 'sexual exploitation of women' which is indicated by the lore related to his temple in the Summer Islands?
With the exception of the Drow, the inhabitants of the Dances with Rogues area DO NOT refer to their gods by name but by title. The Nameless One could well be a local version of the The Forgotten One; which could make him Jergal. Jergal was the original ruler of the Fugue Plane while the Princess could have entered a portal to a layer of the Abyss over which the Old Man has power.
Given that the people "slain at whim" by the Old Man were slain by his fiends while wandering the plane (the Fugue Plane is raided by demons from the abyss who sometimes even attack the city of judgement), there is no indication that he does not actually possess their bodies and souls. And he cannot kill anyone on a whim, only in his own realm is this clearly the case and the Nameless One's realm is obviously not his realm or he would not require fiends to do it for him.
The fact that the Old Man apparantly doesn't give out his name can be explained by him not wanting to be summoned using his real name or because Old Man *is* actually his real name.