An alliterative name is a name in which the first and last names begin with the same sound. In more extreme cases, this can also include the middle name.
Giving a character an alliterative name is one of many ways a writer can make a name more interesting and catchy, which in turn makes the character more memorable to the audience. This is especially important in works with Loads and Loads of Characters, where extra help is needed to differentiate between them.
In comic books, this is especially true of the names of Super Heroes or their close hangers-on. It was a favorite tool of Stan Lee's, since, swarmed with projects, he often had trouble remembering the characters' names, and the alliteration worked as a mnemonic device. (Though it didn't always work perfectly — Lee occasionally referred to "Peter Palmer" and "Bob Banner".)
Of note to writers: Overusing this trope dilutes its effect, particularly if multiple characters have the same starting sounds in their names.
In comic books, the Alliterative Name is often also Two First Names. In cartoons, it goes hand-in-hand with Species Surname.
See Added Alliterative Appeal, for trope titles that do this. See Alliterative Family, for when this is done across an entire family. See Alliterative Title, for work titles that do this.
Please note that Japanese names, though many may seem alliterative to an English-speaking audience, may not convey the same "alliterative power" in their original setting; syllables (and vowel sounds) matter more than letters in Japanese.
Prince John in Robin Hood is apparently fond of alliterative nicknames. He creates at least five of them for Sir Hiss ("silly serpent", "reluctant reptile", "cowardly cobra", "aggravating asp" and "procrastinating python") and has one for Friar Tuck ("corpulent cleric").
John Waters loves this trope. See also Pink Flamingos (Dawn Davenport, Donald and Donna Dasher, Sandy Sandstorm), Polyester (Francine Fishpaw, Todd Tomorrow), Cry-Baby (Wade "Crybaby" Walker, Ramona Rickettes, Wanda Woodward), and A Dirty Shame (Sylvia Stickles, Fat Freak Frank).
Naturally, this caused a storm of Ubuntu jokes after certain statements from Linus Torvalds (just click the "comments" link there).
I Love Bees has James James and his daughter Janissary.
For a bit of potential Fridge Logic, James James ('yeah, J-Squared') is a false name picked by Janissary's father, likely on the grounds that it's so ridiculous and uncreative that nobody would question it.
Professor of linguistics Henry Higgins from Pygmalion by George Bernard Shaw. Also the same character from its musical adaptation My Fair Lady. It's important that his name starts with this sound — thus his Cockney pupil Eliza has to struggle with dropping H's and 'Enry 'Iggins.
A set of 1960s astronaut action figures were led by "Major Matt Mason, Mattel's Man in Space," supported by Lieutenant Long, Sergeant Storm, and civilian astronaut Doug Davis. The lieutenant's given name was Jeff, though.
Homestar Runner: Strong Sad, Pom Pom, Perry Palaroncini & Peacey P. And Stop Sign, Stom Stom, Sickly Sam, Rumble Red, Pan Pan, Szechuan Steve, The Teach, The Thnikkaman, Moth Mouth, Brett Bretterson, Bill Bellamy, Sir Hotbod Handsomeface, Wireless Wizard, Ogg Oggerson, Flash Fight, and Fox Face. Thank you, HRWiki.
The Guild: Vork's real name is Herman Holden. There's also Wade Wei in season 2.
Survival of the Fittest has this in SPADES: Aiden Ambrose, Cillian Crowe, Waldo Woodrow, Paris Persphone, Adam Amato, Andi Ayala, Brendan Bedard, Anthony Ainsworth, Christian Cohen, Debrah and Deliah Dollop, Wade Wilson (not THAT Wade Wilson (but not entirely NOT that Wade Wilson)), Nicholas Nutbrown, Mary McKay, Denise Dupuis, Branca "IT'S A STEAK" Braunstein, Jessica Jones, Bobby Barron, Chadd Crossen, Jonathan Jarocki, Christoper Carlson (a self-insert of Cody Cromarty, his handler), Mike Maszer, Mike Moretti, Gary Griffith, Joss "Jojo" Joiner, Carla Conners, Frankie Fiametta, and Miranda Merchant.
LIS_DEAD seems to have lots of these: Dramatic Detective, Mysterious Mr. M, and Zodiac Zack.
Pete Vs. The Grumpy Gremlins by OchreJelly on deviantART. "Original title: Pete the Plucky Paladin Penguin versus the Gooey Grumbling Grumpy Gremlins. This is kinda what happens when I'm reflecting on things in life, and all coffee'd up."
A few meme characters like Scumbag Steve, Bad-Luck Brian, Good-Guy Greg, and the Foul-Bachelor Frog.
In the classic superhero tradition, the main character of Brennus has the full name of Basileus Bartholomew Balthasar Brant-Blake. One wonders what his parents were thinking, but Basil must have liked it, as his superhero alter ego is called Brennus, continuing the "B" theme.