Given DC's long history, there's no feasable way to compile a complete list of all the charatcers with alliterative names. Taken largely from this List of human superheroes in DC Comics and many helpful comments from Wad Cheber, I have put together what can serve as a decent starting point for DC characters with alliterative names.
Characters:
- Adrian Alexander Veidt (Ozymandias)
- Batman Beyond (Batman)
- Beast Boy (Teen Titans)
- Bernhard "Buddy" Baker (Animal Man)
- Bibbo Bukowski (Superman)
- Billy Batson (Captain Marvel)
- Blue Beetle
- Calvin "Cave" Carson
- Captain Cold (Flash)
- Captain Comet
- Cassandra Cain (Batgirl)
- Clark Kent (Superman)
- Dan the Dyna-Mite (Daniel Dunbar)
- Daniel Dreiberg (Nite Owl)
- Deborah Darnell AKA Star Sapphire (Green Lantern)
- Dinah Drake Lance (Black Canary)
- Doiby Dickles (Green Lantern)
- Felix Faust AKA Dekan Drache
- Francis Flashman AKA Funky Flashman
- Frederick Freeman (New Earth / Captain Marvel Jr.)
- Gorilla Grodd (Flash)
- Guy Gardner (Green Lantern)
- Hank Hall (Hawk)
- James Jacob "Jim" Harper (Guardian)
- Joseph William Wilson (Jericho)
- Karate Kid (Val Armorr - Legion of Super-Heroes)
- James Jesse AKA Trickster (Green Arrow)
- J'onn J'onzz (Martian Manhunter)
- Joker Junior (Tim Drake)
- Lana Lang (Superman)
- Lex Luthor (Superman)
- Linda Lee (Supergirl)
- Liz Lane (Watchmen)
- Lois Lane (Superman)
- Lori Lemaris (Superman)
- Mary Marvel (Mary Willow Batson)
- Mark Mandrill AKA Matter Master (Hawkman)
- Más y Menos (Teen Titans)
- Max Mercury AKA Whip Whirlwind (Freedom Fighters)
- Mirror Master (Flash)
- Miss Martian (M'gann M'orzz/Megan Morse, also Star-Spangled Kid)
- Mister Mxyzptlk
- Moloch The Mystic (Watchmen)
- Preston Payne (Batman)
- Rachel Roth (Raven)
- Red Robin (Robin)
- Robbie Reed (Dial H for Hero)
- Rocket Red (Justice League / Rocket Red Brigade)
- Rodney Rabbit AKA Captain Carrot (New Teen Titans)
- Ronald "Ronnie" Raymond (Firestorm)
- Sargent "Sarge" Steel
- Shiera Sanders Hall (Hawkgirl)
- Silk Spectre (Sally Jupiter / Laurie Juspeczyk)
- Silver St. Cloud (Batman)
- Tex Thompson (Mr. America)
- Vicky Vale (Batman)
- Wally West (Kid Flash)
- William "Bill" Benjamin Brady (Watchmen)
- Wonder Woman (Princess Diana of Themyscira)
- Zatanna Zatara (Hawkman)
Group names:
- Freedom Fighters
- Secret Society of Super Villains
- Secret Six
- Seven Soldiers of Victory (AKA Law's Legionnaires)
- Suicide Squad
- Teen Titans
- The Terrific Trio
- Hero Hotline
Plus loads and loads of random people from the List of DC Comics characters:
- Aa (Green Lantern)
- Abdul the Arab (Quality Comics)
- Ace Archer (The Green Arrows Of The World - Japan)
- Bowman of Britain (The Green Arrows Of The World - United Kingdom)
- Bowman of the Bush (The Green Arrows Of The World - Africa)
- Ace Atchinson (Young Justice)
- Sue Storm (Ace Storm - Challengers of the Fantastic)
- Agent Arrhnyr (Action Comics 534)
- Agent Axis (Boy Commandos / World's Finest Team)
- Aisha al-Fadhil (The Losers)
- Alan Armstrong (Spy Smasher)
- Albart of Ancinor (Atlantis Chronicles)
- Albert the Artist (Action Comics 428)
- Ana Ala (Ale - Superman: The Man of Steel, #127)
...
From Why Are There So Many Double Initials in Comic Books?
What is the L. L. connection for Superman?
A remarkably large number of characters in the comics have the initials L. L. Most notable are Lex Luthor, Lois Lane, Lana Lang, and Lori Lemaris. A rumor says that these names were chosen because Joe Shuster's first girlfriend had the initials L. L.