Fake Twin Gambit

This is where a character, for some reason or another, pretends to be their own (nonexistent) identical twin. It could be for disguise, or to see how their friends really think of them. Success rates vary.

See also Twin Switch, Backup Twin. Subtrope of Invented Individual.

Examples of Fake Twin Gambit include:

Anime and Manga

Subverted in Higurashi no Naku Koro ni. Keiichi thinks that Mion is using this trope, pretending to be "Shion" to be able to act differently than how she normally acts... until Keiichi and Shion run into Mion.
- Of course, the real Shion doesn't care for Keiichi in the least, but the whole matter gets complicated really quickly, but that's a different trope. At the very least.
Played with in Haruhi Suzumiya. Kyon and Mikuru pretend that Mikuru is "Michiru" - because the "real" Mikuru is still around (blame time travel) and "Michiru" needs to hide from herself.
Maruko wants to do this by moving a mole in Chibi Maruko-chan.

Comic Books

In Daredevil, Matt Murdock (Daredevil's secret identity) pretended to be his own non-existent twin brother Mike Murdock to trick his friends into believing that "Mike" was Daredevil, after they began suspecting his identity. This was back in the Silver Age of comics when even Daredevil wasn't a very realistic series.

Film

A weird version of this happens in The Prestige, where both twins pretend to be the other twin at times.

Literature

Mercedes Lackey's Born to Run has one mechanic doing this as a practical joke to get back at a pair of elf twin brothers, who he had thought were just one person.
Hercule Poirot creates an imaginary twin brother named "Achille" in The Big Four - a parody of Mycroft Holmes, in fact.
In Raymond Chandler's essay "The Simple Art of Murder", he gives several examples of excessively contrived puzzles from the British whodunnit tradition, including a novel in which a Fake Twin Gambit is used by the murderer to effectively frame the victim for his own murder (by doing him in while he's being the twin, so that it looks like murdered his twin and then went on the run).
Vorkosigan Saga: Miles Vorkosigan used a variation on this to cover for his "Admiral Naismith" identity, by spreading a rumor that Naismith was his clone. Between that and his real clone-brother Mark, he managed to create the impression for a while that there were three of him running around.

Live-Action TV

In 'Allo 'Allo!, after Rene faked his own death, he came back pretending to be his own twin. This received frequent Lampshade Hanging during the series.
Jane from Coupling:

Jane: I once went on holiday and pretended to be twins. It was amazing fun. I invented this mad, glamorous sister and went around really annoying everybody. And d'you know, I could get away with anything when I was my crazy twin Jane.
Sally: But you're Jane.
Jane: Kinda stuck. It's a long story.

The Janitor tries to do this in Scrubs as a prank on JD. JD isn't fooled for a second, causing the Janitor to ramp things up with more and more ridiculously phony "evidence" that he has an identical twin. In a last act of desperation, he claims that his brother is waiting for him at the bottom of the elevator, and when the doors open to reveal nobody he admits, "OK, I don't know what I thought was going to happen." It was perhaps the only time the Janitor failed to get the better of JD.
Happens in the Tales from the Crypt story "Split Personality". A conman fools a pair of reclusive and wealthy identical twin sisters into falling for him and his invented twin brother so he can collect on their fortune. When he accidentally reveals the ruse via his own carelessness, the sisters are very upset and decide to ensure that each gets her fair share for once -- with the help of a chainsaw.
Played with on iCarly: Sam spends an episode trying to convince Freddie that she has a twin sister (who Freddie ends up going on a date with), before finally admitting that it was a trick. And then after Freddie leaves, Sam's sister comes up in the elevator.
Barney, from How I Met Your Mother, has been mentioned using this trope when trying to trick women into sleeping with him again after having already seduced and abandoned them. The audience has never been shown him actually doing it, but at one point an ex' assaults him while calling him by his fake brother's name, "Blarney"
- The final stage of his "Lorenzo Von Matterhorn" play was to be faking Julio's death and then seducing the woman again as his brother, Julio Von Matterhorn.

Web Comics

Starslip has Vanderbeam trying this. Poorly.
In PvP, side character Binwin tries to invoke this trope here.

Western Animation

Angelica does this on an episode of Rugrats.