Examine the theme of your character
Even people who don't roleplay often have a sense of who their characters are as people. Do you consider your character a tank, a bull-hearted defender of friends and allies? Is your character a sly rogue, clever and sneaky? Getting a grip on the themes and playstyle of your character can go a long way toward providing name inspiration.
Taking the time to put those ideas and themes into words will help you create a list of possible names for your character. An obvious example is everyone's favorite dragon brother, Nefarian. You couldn't have Nefarian without nefarious. The game itself uses this kind of roundabout name conversion all the time. Sinestra obviously stems from sinister.
Dig around for a good adjective to describe your character, and then see if any of the variations appeal to you. Here's some examples:
Valiant can be Valiont, Vallant, Valiance.
Sacred could become Sacrad, Sacredde, or even Dercas.
Wrathful grows into Rath, Wrouth, or any other variation.
As a general rule, you probably want to keep the sound
of the name the same. Even though one of our examples is a reverse spelling of the same word, someone else reading your characters name should recognize the root word. Aim for something that sounds like the original concept so that you can evoke the theme you want.
Don't be afraid to look at other languages when you're searching for good words. Plenty of opportunity lurks outside of your native tongue, and you can get some really creative options that way.
Describe the physicality of your character
There's a reason everyone talks about Dwarves named Longbeard and Gnomes called Cogspinners. These names reference distinct, visual reminders about the races. This is also why you see a half-million Tauren with names using hoof, horn, and udder.
Putting together a good name that references physical traits is actually a little more difficult than you might think. Describing a Night Elf as something like Inkface probably won't get your point across.
Here's some good, archetypical words you can use to describe each race:
Blood elf Gold, hair, eyes, grace, spire
Dwarf Beard, axe, brew, ale
Draenei Light, shine, heal, hew
Gnome Cog, gear, steam, whisker, pate
Goblin Boom, bomb, fire, crash
Night elf Wood, dusk, stride, eve
Orc Fang, dark, hammer, scream
Tauren Hoof, horn, field, plain
Troll Tusk, pipe, mojo, tall
Worgen Fang, tooth, claw, fur, paw
These are all examples, of course. But if you're without any other inspiration, try slapping some descriptive phrases in front of these suffixes and see how it works out. Bloodhair, Darksteam, and Lighthoof all await your adventuring pleasure.
Draw from legend
Lastly, reach out to some historical peoples and co-opt their legends for use in game. Ragnaros won't mind.
Obviously, the most popular legends and the straight-up names won't be available for use. I can't imagine anyone scoring Lancelot or Morgana at this late point in the game. But you can tinker with the names and pull out something more unique.
Morganos might be available on your server, or even Zeusian, Herator, and Lancell. Just like using a theme to describe your character, try to keep your unique version evocative of the original.
Take your time
The most important thing when desigining your character's new name is to take your time. Don't rush into something you might regret just because you're in a hurry. You can change your name later, of course, but save yourself a little cash and get the name right from the beginning.
Visit the WoW Rookie Guide for links to everything you need to get started as a new player, from how to control your character and camera angles when you're just starting out, to learning how to tank, getting up to speed for heroics and even how to win Tol Barad.