Tex Thompson, aka "Mr. America" and "Americommando", a spy-smashing superhero introduced in Action Comics #1 along with Superman. He's been revised and retconned several times since then.
Bruce Wayne once had a series of alliterative romantic interests, including Vicki Vale (played by Kim Basinger in Batman) and Silver St. Cloud. While Batman's own name doesn't directly count, one of his common monikers, "the Caped Crusader", is also alliterative.
Cassandra Cain, the third Batgirl. Cass went on to use the hero name Black Bat after leaving Batgirl to Stephanie Brown in Batgirl (2009).
The Attack of the Annihilator storyline has Bob Barton, one of the colleagues of Barbara Gordon in the "Humanities Research & Development" Center.
Katherine "Kate" Kane, the Pre- and Post-Crisis Batwoman. Post-Crisis, Kate Kane takes this an extra step with the nickname "Candy" from her time as a cadet boxer.
The Red Robin title, which was first used by an Elseworlds version of Dick Grayson before being brought to the main continuity as a costume and code name for Jason Todd and being taken up by Tim Drake after Todd abandoned it.
Hamilton Hill and Charles Chesterfield, former mayors of Gotham City.
Deathstroke: Deathstroke had a brother Wade Wilson, AKA the second Ravager, as a joke on the real name of Deadpool who was originally a Deathstroke Captain Ersatz.
And Firestorm's supporting cast and rogues' gallery has a few. Jefferson Jackson, Henry Hewitt (Tokamak), Mai Miyazaki (Naiad), Quentin Quayle, David Drake (Typhoon), Cliff Carmichael, Doreen Day...
Doiby Dickles, sidekick to Alan Scott, the first, Golden Age, Green Lantern. Opposing Scott were Steven Sharpe (The Gambler), Molly Mayne (Harlequin), and Crusher Crock (Sportsmaster).
Kid Eternity: Characters with names that are alliterations are frequent in the 1940s comics, with just some examples including Dan Doldrum, Murder Marton and Killer Karf.
Martian Manhunter: J'onn J'onzz/Martian Manhunter and M'gann M'orzz/Miss Martian, his Distaff Counterpart from Teen Titans. M'gann M'orzz is named after Megan Morse, a friend of Geoff Johns...but he probably chose it for its alliteration anyway.
Metamorpho: Simon Stagg and his daughter Sapphire Stagg
Miracleman: Mike Moran, Marvelman/Miracleman and Dickie Dauntless, Young Marvel/Miracleman
The Multiversity: Earth-8 has a couple of examples; given that that world is based on the Marvel Universe this is to be expected.
The Multiversity #1:
Doctor David Dibble, the human alter-ego of The Behemoth.
Plastic Man: Woozy Winks, sidekick of Plastic Man.
Sarge Steel: Sargent "Sarge" Steel, one of the Charlton Comics heroes purchased by DC. ("Sargent" is his name, not a rank.) Originally a hard-boiled detective/spy-smasher type, he became a government official in charge of many of the DCU's superhero-related agencies.
