Daniel Pinkwater's Slaves of Spiegel features a literal Cooking Duel between three Identical Strangersnote sort of — there's the minor point that they're from three different species, and said species don't remotely resemble each other, but besides that, totally identical who are supposedly the best chefs in the universe. They are named Steve Nickelson, Evest Linkecsno, and Tesev Noskecnil.
A Face Without a Heart by Rick Reed is a modern day version of The Picture of Dorian Gray; its protagonist is named Gary Adrion, which is an anagram of... Dorian Gray.
The last book has a psychic vampire named Dandelo who lived at Odd Lane. He at least has the sense to add an S to the sign pointing to his house, making it spell Odd's Lane, though technically, the S and apostrophe on the sign would make it an even better anagram: Dandelo's.
For a while before the last book or two came out there was a lot of speculation on the web regarding the way that "Finli O'Tego" (which even looks like a frickin' anagram) could be rearranged into "It of Legion" or "Legion of It".
The Da Vinci Code's main villain is named Sir Leigh Teabing. The pseudo-historical claims The Da Vinci Code is based on were made several years earlier in Holy Blood, Holy Grail by Richard Leigh and Michael Baigent (Baigent=Teabing)
In another Michael Crichton book, Digital Fortress, the main characters are in contact via e-mail with someone who they know only as his pseudonym "North Dakota". His e-mail adress user-part is N.DAKOTA. At first he seems to want to help them but it turns out to be the main villain, whose name is Tankadonote A bit awkward was that this character was Japanese-born, but Tankado is not a real Japanese name, despite its reasonable veneer of plausibility.
Stephen Fry's novel The Stars' Tennis Balls has a plot very similar to The Count of Monte Cristo. The principal character is Ned Maddstone (anagram of Edmond Dantes), who reinvents himself as Simon Cotter (anagram of Monte Cristo), and the figures he takes revenge on include Barson-Garland (Baron Danglars), Gordon Fendeman (Fernand Mondego) and Oliver Delft (de Villefort). (The Count's other victim, Caderousse, gets "translated" as Rufus Cade) and his ex-girlfriends name Mercedes get translated into Portia, wich sounds like Porsche and both Porsche and Mercedes-Benz are name for cars.
There's a minor character in Lolita named Vivian Darkbloom (an anagram of Vladimir Nabokov). This is a common occurrence in Nabokov's books, with the surname changing at times to Bloodmark, Calmbrood (the c-k anglicization), and even once a "Mr Vivian Badlook".
Lolita also involves a section wherein Humbert chased Lolita across the country and finding that that her mysterious "abductor" continues to taunt him by using obvious pseudonyms in hotel registries, one being Ted Hunter, Cane NH. This is an anagram of Enchanted Hunter, a play that Lolita had once acted in. Her "abductor" is later revealed to be the play's author.
Nabokov's Pale Fire is written by a man named Kinbote who may or may not be insane. One theory as to his identity is that he is actually Russian professor Eugene Botkin and has invented a completely new persona.
In The Hostile Hospital, Klaus and Sunny discover Count Olaf hid Violet Baudelaire as a patient in the titular hospital - under an anagrammed name. Lampshaded in that there are half a dozen other names that coincidentally are almost anagrams of "Violet Baudelaire". Also, going back to The Bad Beginning, the author of the play is Al Funcoot, an anagram for Count Olaf.
Given the series' emphasis on codes and secrecy, anagrams are frequently used throughout the series in general. A list of most of the significant anagrams used in the series can be found on the Lemony Snicket Wiki.
Edward Gorey frequently makes use of anagrams of his own name in his books, including "Ogdred Weary," "Dogear Wryde", "Regera Dowdy", "D. Awdrey-Gore", "Waredo Dyrge", and "E.G. Deadworry", the last three coming from the same story. During the later years of his life, Gorey in fact drove a white vintage car with Massachusetts license plates saying "OGDRED"; Gorey's last compilation book, Amphigorey Again, features a list of (all?) 31 of Gorey's anagrams and pseudo-anagrams under the heading "In fond collaborative memory".
The Haruki Murakami novel Dance Dance Dance has a minor character named Hiraku Makimura, who is also an author.
The titular female vampire of Carmilla is also known as Millarca and Mircalla, her original name. Apparently it's vampire tradition to alter your name every "lifetime."
In the Past Doctor Adventures novel Business Unusual, the computer game company SeneNet is a front for the Nestene Consciousness.
In Original Sin, the villainous company is Interstellar Nanoatomic ITEC (ITEC being the 30th century version of Ltd. or Inc.), which is an anagram of International Electromatics, a company the Doctor's dealt with before.
In Lloyd Alexander's Westmark series, the conman Count Las Bombas's alter egos are near-but-not-quite anagrams of Las Bombas and of each other, including "Dr Absalom" and "Mynheer Bloomsa".
An odd metatextual example: in Margaret Weis & Tracy Hickman's The Death Gate Cycle, a crazy, absent-minded wizard named Zifnab appears. He is an obvious Expy of Fizban, a character Weis & Hickman created in their Dragonlance books. Since Wizards of the Coast owns Dragonlance, they were unable to use the character in their own original work. The same character, this time called "Zanfib," shows up again in Weis's Starshield novels.
In the Gemma Doyle Trilogy, the secret society, The Order, has its members make anagrams of their names. When the three main characters try their former teacher's name, Hester Moore, they get absolutely nothing but gibberish. But when Gemma learns that Miss Moore's middle name is Asa, she makes an anagram for the name Sarah Reese-Toome, who is known to be Circe, the antagonist for the series. Naturally, this leaves Gemma in a state of Heroic B.S.O.D. for a couple chapters while she realizes how badly she has screwed up by playing into Circe's Kansas City Shuffle.
In F. Paul Wilson's Repairman Jack novels, the Big Bad of the series tends to hide behind anagrams for the name "Rasalom" — which is not a name you should speak aloud.
The central idea behind Norma Schier's "Anagram Detective" stories. Each is a pastiche of a popular mystery series. The pen name of the author and the names of the main characters are anagrams of the names of the real author and the series characters. Places and supporting characters get names that are anagrams of their roles in the story. After the story all anagrams are listed.
The Christopher Pike young adult mystery novel Last Act features a play written by the murderer solely to set up the murder; the pseudonym she uses as playwright (deliberately, as dramatic flair and a challenge) is an anagram of her name.
Dennis Lehane's Shutter Island resolves into a number of anagram names.
In Ira Levin's Rosemary's Baby, Rosemary hears about a warlock named Steven Marcato. One of her neighbors is named Roman Castevet. The plot thickens...
The Devil May Cry novel has a green-suited, heavily bandaged mercenary carrying a Katana by the name of "Gilver" (switch the syllables around) show up to be Dante Tony's Rival.
While Lief and co. gathered the Seven Gems, they're also searching for the hidden heir to the throne, a descendant of Adin. During their quest, they meet Dain. He's not the real heir, but an Ol 3 intentionally using that name to infiltrate the Resistance.. Dain also tells Lief that his mother's name is Rhans, the name of the heir's mother is Sharn.
In the second book of the third series, Lief realizes that a set of notices has been faked when it occurs to him that they all contain an anagram of the phrase "seek the nomad"
The Redwall series features this as a plot point in the first book, with "I am that is." being a recurring line in many of the older writings the main characters discover. ("Am that is" is an anagram of the protagonist's name, Matthias.)
Gulliver's Travels tells of a country where the "anagrammatic method" is applied to people's letters so they can be accused of spying. This country is "the kingdom of Tribnia, by the natives called Langden."
In Harry Turtledove's World War series, Sam Yeager uses the alias Regeya to access The Race's computer network. After he is discovered, he switches to Maargyees.
Captain Eden of the Star Trek: Voyager Relaunch was told by her "uncle" Jobin that she was rescued from the planet Sbonfoyjill. She eventually realized, after trying to locate it in databanks and finding nothing, that sbonfoyjill is an anagram for "Jobin's Folly".
In the Discworld novel Thud!, Sam Vimes recognises that the mole in the Watch is Sally von Humpeding when he intercepts a message to her spy master. It is signed "Aicalas", which he realizes is the name "Salacia" written backwards in true "Alucard" vampire style.
Soul Seekers: Cade and his twin brother Dace's names are anagrams of each other.
An Abundance of Katherines: Colin, the main character, is an anagram savant (among other things). Lucky for him, because anagrams turn out to be an unexpected plot point.
In The Shadow pulp novel The Romanoff Jewels, one of the main villains was named Frederick O. Froman. He chose this name himself, as his actual surname was "Romanoff" and a he was distant relation to Czar Nicholas II. "F.O. Froman".
The Ravenloft novel I, Strahd features a band of mercenaries whose names are all anagrams of Blake's 7 characters.
In the German pulp horror/fantasy/SF series Professor Zamorra this is a personal quirk of the demon lord Asmodis when it comes to choosing names for his cover identities. It's not always a strict anagram (although he's prominently used both 'Sid Amos' and 'Sam Dios' respectively for years), but some 'clever' hint to his true identity will usually be there.
In the Goosebumps2000 book "Headless Halloween" Brandon encounters a boy wearing a mask identical to his own named Norband. The Blogger Bewarereview comments "The kid he encounters is named Norband— I guess Nodnarb was too on the nose? Norband invites Brandon to a Halloween Party— or is it really a Lonewhale Atpry?!?!"
This trope is Older Than Steam: One of the first picaresque novels in Germany was by Christoffel von Grimmelshausen writing under the pen name German Schleifheim von Sulsfort, and the hero is Melchior Sternfels von Fuchshaim.