Façades
A major theme of Double is the contrast between characters' private lives and public faces. For the majority of the novel, Chap is playing the role of Cassiel Roadnight, a clear example of personality/persona dualism. To everyone else, he is the lost son returning home, the prodigal miracle. On the inside, however, he is anything but: an orphaned teenager lying his way into the comforts of a family.
Chap isn't the only character with a façade. Frank, most notably, puts on the persona of a successful, honest businessman who cares for his family and his work in equal measure. Underneath the role he plays, though, lurks a much darker character: a robbing murderer who would kill his own brother to preserve his secret. The juxtaposition between his public persona and his true character is perhaps even more striking than that of Chap.
Other characters wear public personas in the same way as most people do; they hide particular facts of their personalities from the public. Edie, for example, pretends not to care for Cassiel but betrays herself through her actions; Cassiel clearly wore the façade of a decent human being while blackmailing his brother; and even Helen hides things from her family. The only character notable for not having a façade is Floyd, whose eccentricity is visible even at first glance.
Parasitism
Many of the characters in the novel live in a way that obtains benefit for themselves by taking advantage of the circumstances of others. The most obvious example is Frank, who gained his wealth by robbing a rich old man and has been living off that money ever since. In this case Frank is acting as a parasite, feeding off someone else's life.
Cassiel, before he died, also lived parasitically; he blackmailed Frank into giving him parts of that fortune as well. Rather than turn his brother in or passively allow his parasitic life, he chose to feed off the parasite himself, making an income the easy way rather than the honest way.
Chap's parasitism seems less egregious but is there nonetheless; he quite literally lived someone else's life for a while. He fed on Cassiel's family, home, and resources while working for none of it himself. By revealing the deception of his brothers and revealing his own true identity, though, he might have made up for it.
Identity
From the very beginning, Chap's identity has been in a nebulous state. He was an orphan of unknown origin, living with a figure he knows as his "Grandad" in a large, mostly empty house. When his grandfather was injured, though, he gave him news that shook his perception of his own identity: they weren't actually related, a teenage girl dropped him off at his house after she burned a house down, and that's all he knew. From then until the end of the novel, Chap's search for his own identity took shape and eventually reached its conclusion with the realization that he was, in fact, Damiel Roadnight.
Identity is an issue for other characters in the novel, as well. Mr. Hathaway, or "Grandad," constantly lived in the belief that his social anxiety prevented him from doing anything of worth. His perception of his own identity limited him unnecessarily.
Edie also frets over her identity; she isn't sure if she should go to college, or if her identity as an artist is the most important one, or who she is now that Cassiel has returned. Her role in the family underwent a revolution, and so did her sense of identity.
