One obvious example is Ebony Dark'ness Dementia Raven Way from My Immortal. (Note the gratuitous apostrophe, and that "Dementia" is quite a lovely-sounding name so long as you ignore what the word means.)
Who will always be lovingly referred to as Enoby by fans and haters alike.
Even canon characters get new awesome names. Like Harry Potter being Vampire and Voldemort being renamed Satan Bombodil Andorson!
And then, you've got Mary Sues with names like "Chihuatlan Razortalon." Sure, "Razortalon" fits the model...but "Chihuatlan" invokes small yappy lapdogs rather than the exoticism for which the author was no doubt shooting.
Detsniy Off Skiword has given his characters such names. Most notable are Ronin, from The Hoen Jorneys, and Dusk, from Avance Wars 3 Yelow Comet Defence, who outright says he changed his name to Dusk since his original immigrant protection name of Darkness wasn't cool enough.
In The Mad Scientist Wars we have the Tinker family, who all have this. For instance Andrew Omega-Particle prince Risk Tinker, or his son Frederic Zeta Risk Raize Tinker. This goes back pretty far- for instance, Grandpa Florian Blitz Viktor.
A character in numerous fanfics on the Phineas and Ferb Fanon Wiki is named Goldfish Darkskull.
All the Fullmetal Alchemist characters have ridiculously cool names. In the Elemental Chess Trilogy fanfic series, Riza Hawkeye gets an extra one. After she marries Roy Mustang, the men of their unit feel awkward calling her Hawkeye, but they also can't call her Mustang, so they refer to her by the affectionate nickname "Ladyhawk."
Frozen fic What About Witch Queen? has side-character called Bjorn Berg, who doesn't sound like an example until you realize that his name means Bear Mountain. (It may also double as a shout-out to Swedish-born tennic champion Björn Borg.
Who is promptly nicknamed by the four "Ass," "Asshole," Santa's Ass," and "Jeez-Ass" (after he gets resurrected).
The Dilgar War has captain Manly Power. At first the crew of the Space Race can't believe it, then they verify it and realize his crew has to call him Captain Power, and declare it the coolest name ever.
The Alarmaverse: Ditzy Doo is actually short for Detsella Renombrada Morningdew. And her dad's full name is LaMontagne Burningspear Morningdew, but he normally goes by LaMonte Doo.
Aesir: Cross Wars: The Hero and the Deuteragonist are named Azrael and Azazel respectively. Being based off Norse Mythology, the names Odin, Hel, and Loki are pretty cool as well. However, the coolest name in the story has to be freaking Crushadion.