Battlefield Heroes loves this: Buccaneer Bay, Coastal Clash, Seaside Skirmish, Victory Village... and that's just (ALL of) the levels! Burning Bullets, Troop Trap, and almost all of the weapon names: Greg's Greasy Gun, Wolfgang's Wonderful, Florenz's Flurry, etc.
In DKC1 to DKC3, in addition to levels, the worlds nearly all have alliterative names, with names like Monkey Mines, Vine Valley and Gorilla Glacier, while the second game has Gangplank Galleon, Crocodile Cauldron and Krazy Kremland.
Every level in Donkey Kong 64. Jungle Japes, Angry Aztec, Frantic Factory, Gloomy Galleon, Fungi Forest, Crystal Caves, Creepy Castle, Hideout Helm. Even the majority of the minigames have alliterate titles. Also arenas, one of the shooters, and most of the Cranky abilities (a couple of the exceptions go with rhyming instead).
Donkey Kong Country Returns continues the alliterative level names with stuff like Poppin' Planks, Rickety Rails, Muncher Marathon and Furious Fire.
It extends to the names of certain characters as well: Cranky Kong, Candy Kong, and King K. Rool.
Gailardia Galan Gardios from Tales of the Abyss. You probably know him better as Guy, though.
Not characters per se, but a number of the starting scenarios in the X-Universe games have these. Some examples are "Tormented Teladi," "Boring Boron," and "Lost Lar."
The Jump Start edutainment games series introduced 4 characters in JumpStart Preschool to which this trope applies: Casey Cat, Eleanor Elephant, Kisha Koala, and Pierre Polar Bear. Too bad Kisha was retconned into a tiger in 2005, ruining the Added Alliterative Appeal! (Pierre also got turned into a different species, but the alliteration was maintained - he became a panda.)
Toontown Online has lots of denizens that have alliterative names such as Clerk Clara, Fisherman Furball, Tim Tailgater, Nina Nitelight, and Fast Freddie. Incidentally, Fast Freddie's building takes this to the extreme: Fast Freddy's Fretless Fingerboards (Fabricated From Figured Fir!).
In addition to the series and game titles, most of Rage Racers in-game music tracks are alliteratively named ("Silver Stream", "Mech Monster", "Volcano Vehicle", etc.), with the exception of "Mathemabeat", "Industria" and "Stimulation".
Buster Badshot, from classic arcade game Cheyenne by Exidy.
Some of the levels in the Banjo-Kazooie series: Mumbo's Mountain, Clanker's Cavern, Mad Monster Mansion, Cloud Cuckooland, Terrarium of Terror.
Dungeon Crawl: The slime god Jiyva has a randomly created, alliterative second name, reflecting his amorphous nature.
Ensemble Stars! has Sengoku Shinobu. Mikejima Madara, Hidaka Hokuto,Kiryu Kuro, and Nito Nazuna.
Moshi Monsters has several characters with alliterative names, including Bucky Barnacle (although he goes by Buck E. Barnacle or Captain Buck), Tamara Tesla, Agony Ant, Handy van Hookz, Jaunty Jack and Buster Bumblechops.