Kayfabe Music

The band is real, but the singer is a more or less fictional character. Same may go for the rest of the band.

There are two categories of examples: "Real Life Music" for bands that exist in real life, and "other media" for bands that are a Show Within the Show.

Just like with wrestlers, a Kayfabe singer's real identity may be an open secret. That is, not secret at all but not polite to talk about in context. The fans are likely to be outraged if the singer goes out of character during an interview.

Compare "Kayfabe" from Professional Wrestling. One subtrope is Robot or Spaceman Alter Ego. Contrast Anonymous Band, where the mucicians simply hide their identities, and Fake Band, where the band itself is fictional.

Real Life Music

 * In Blutengel the singers are vampires.
 * The band Rolandz has developed a quite solid discography and even been on tour. It's singer, Roland, is a character from a comedy movie. The real singer is the same actor who played Roland in that movie.
 * Manowar consists of really manly men, fantasy heroes who are always ready to kill anyone. With STEEL, of course.
 * Lordi are monsters... who have sued to bury images of them out of costume.
 * Markoolio play this on two levels. His first persona is this cool playboy, gangster, warrior, expert soccer strategist, and so on. However, this facade breaks all the time, especially since his own chorus are disloyal to him and frequently rat him out to the audience - exposing him as the total failure and Small Name, Big Ego that he really is. Of course, this "real person, under the mask" is just as fabricated as the first level.
 * At the live Vocaloid concerts, the band is real enough, but the lead "singer" is a projected image (and not really a singer at all).
 * Daft Punk's persona is of a couple of robots.
 * Lady Gaga went to her little sister's graduation in full Gaga regalia. She later said that she considers her entire life to be part of her 'character'.
 * Members of the German band Coppelius usually play their XIX-century aristocratic personas in public.
 * Kraftwerk are robots, who became less human as time progressed.
 * GWAR has a long backstory about them being aliens banished to Earth, and like Lordi are never seen out of costume.
 * Devo has gone through a few permutations of this; it's essentially them, except with sci-fi bases, an idiot manager that doesn't understand them, a giant baby (Booji), and their...uh...leader, General Boy. They always did claim to be a corporation, which got a lot funnier in the mid-90's when they reformed as a soundtrack company.
 * And then there's bass player Jerry Casale's side-album as Jihad Jerry, essentially Stephen Colbert as a Muslim blues musician.
 * And then there's the Gorillaz, who take this to the max (namely they're a Band Toon in the real world, and that's not even going into their individual backstories).
 * Buckethead is in fact the guitarist from...Guns 'n' Roses, I think. On stage, however, he is a frightening man with a KFC bucket on his head and a thoroughly disturbing oeuvre.
 * Industrial Metal artist Mortiis, for a long time, was never seen without his troll mask on, with it's pointed nose and big ears. In 2005 for his album The Grudge his mask took on a more artificial appearance, looking like it had been stitched and stapled to his face. After that, however, he finally removed the mask.
 * Singer Emilie Autumn seems to always be in character as Emily-with-a-Y from her book to some extent.
 * Stovokor is a death metal band consisting entirely of Klingons.

Comic Books

 * In Pondus, Pondus believes that a certain rock band truly lives the creed of "Drugs, Sex & Rock'n'Roll". In one strip, the band is shown working out and eating healthy food. Suddenly their manager come in and yell at them that the journalists will be there any minute. And thus, they quickly trash themselves down to look as if they have been partying and boozing up all night. Then the scene switches to Pondus and his wife watching the television. A journalist is (or probably rather is pretending to be) surprised that the band members manage to stay healthy with this lifestyle. The singer explains this with "It's rock'n'roll", baby. It becomes a lifestyle." and Pondus tries to get his wife to accept this message as gospel.

Film

 * In Tropic Thunder, Alpa Chino is a rapper

Live Action TV

 * Law and Order SVU used this twice. Two big scary musicians, suspected of horrible crimes.
 * One is a black "gangster" rapper suspected of rape/murder on a white woman. However, he he is actually quite naive and have no experience of real crime, his gangster persona being nothing more than a keyfabe persona.
 * The other is a "vampire" who is afraid of getting HIV from real blood.

Western Animation

 * Lead-singer Jem from Jem and The Holograms (is a holographic projection protecting the identity of Jerrica, the company owner).
 * In Arthur, the band Binky is made of up Hologram musicians and synthesized sounds. Apparently an open secret, as the episode on the band has them materialize from nowhere during a live performance.