Max Trope

"Max" is both a name (short for Maxwell, Maximilian, or Maxine) and also short for "Maximum", leading to all sorts of names both punny and awesome. See Cutscene Power to the Max, Catch Phrase to the Max, Alice Allusion and Everything's Better with Bob.

Punny Versions

 * Max Headroom
 * Max Payne
 * Pv P: Max Power
 * And on The Simpsons
 * Max Havoc: Curse of the Dragon

Comic Books

 * Sam and Max
 * Maxima, Queen of Almerac, a Superman villain.

Film

 * Max Keebles
 * Max Zorrin
 * Max Rockatansky
 * Maximus Decimus Meridius
 * And Maximus the horse
 * Max Aldorfer, protagonist in Liliana Cavani's film The Night Porter. He is a reformed Nazi officer who had a sadomasochistic relationship with a concentration camp inmate.
 * Maximillian, whose master was coincidentally played by Maximillian Schell.
 * Maxim Brailovsky

Literature

 * Maximum Bob
 * Maximum Ride
 * In The Hitchhiker's Guide to the Galaxy the fat cat boss of Megadodo Publications (publisher of the Guide) is named Maxelcat.
 * Also, MaxiMegalon
 * Maxim magazine, though it may not count as literature.
 * It's named after the Maxim machine gun.

Television

 * Maxwell Smart
 * Ultraman Max
 * Maxwell Sheffield
 * Maximillian Arturo

Theatre

 * The protagonist in Carl Maria von Weber's opera Der Freischütz

Video Games

 * The Beast Master hero in Warcraft 3 can have several names, one of them Maxx Rocmane.
 * Max Payne, of course.
 * Maximilian, one of the Villain Protagonists in Evil Genius.
 * DDRMAX and the song "Max 300".

Web Original

 * Three different Maxes from Survival of the Fittest: Maxwell Crowe, Maxwell Lombardi, and Max Neill.

Western Animation

 * Max and Ruby.
 * Max Power
 * Max Steel
 * The Maxx
 * Mighty Max
 * Montana Max
 * Max Goof
 * Fantastic Max

Real Life

 * Jazz drummer Max Roach
 * Max Factor
 * Max Planck
 * Max Weinberg
 * Max Weber
 * Max Brooks
 * Viva Max! - Mexican General Maximillain de Santos retakes the Alamo, in 1969.
 * Max Ernst
 * Max Schreck, German actor famous for playing Count Dracula Orlof in the film Nosferatu.
 * Named after the above, industrialist Max Schreck in Batman Returns.
 * After the Real Life fat cat publisher Robert Maxwell.
 * Staff Sergeant Max Fightmaster, who may have has the single greatest name ever given to a man.
 * Max Venturi, LAMBOURGHINI TESTER!
 * Max Brenner is a guy who owns a chain of chocolate themed restaurants.
 * He doesn't actually exist; the name of the chain is an amalgam of the two founders' names.
 * Max Baer was a boxer, his son Max Baer Jr. played Jethro on The Beverly Hillbillies.
 * Max Steiner
 * Max Von Sydow.
 * Minolta made a camera series called Maxxum. (Although in Japan it was marketed as Alpha and in Europe as Dynax. When Sony took over Minolta they changed the name to Alpha worldwide.)
 * Subtitling company CaptionMax is named for its founder, Max Duckler, who clearly saw the potential of this trope in naming the company after himself.