"I Need Help Naming My Character!" - What To Do When You Don't Know What To Name Your Character
I encounter so many people who are stuck on what to name their characters, so I've decided to write down all of my advice and put it onto one page.
If you're writing a fanfiction, pay attention to the names of the canon characters and see if you can notice any patterns or themes. Characters in The Hunger Games tend to have names relating to nature, or something otherwise important or relevant to their districts of origin. Characters in Harry Potter usually have meaningful names, but also have alliterative names, names that sound whimsical or slightly silly, or even themed names (the Black family having a tradition of naming children after celestial objects). Humans in Homestuck have four-letter first names and six or seven-letter surnames.
If your story is set in the future, see the article Names of the FUTURE!!!.
If your story is set on Earth as we know it, consider your character's culture, ethnicity, location, time, and socioeconomic status. You're probably not going to find many 18th century Japanese lads named Jefferson, nor many 20th century white upper-class Minnesotan lasses named Tyreesha, nor English Cockney girls named Seraphina Lorraine Windsor.
Meaningful names can be fun (and give your readers something fun to discover or notice), but don't get so caught up in finding the "perfect" meaning that you end up with names that sound completely inappropriate or out-of-place. For example, naming your anglo-American teen "Raiden" because you want a name that has something to do with thunder is a bad move. On the other hand, you could name the character Franklin in reference to Benjamin Franklin and his kite experiment and/or the fact he invented the lightning rod.
With any setting where the characters wouldn't be speaking any Earth-languages (eg, fantasy or science fiction settings), you have a lot of leeway. However, it's not particularly wise to start chucking out whatever syllables sound sort of alien and fairly name-y to you. Most cultures have rules of some sort about names, even if they're unwritten and largely unconscious. For example, English-speakers tend to think of -a, -ia, and -ette as being proper endings for women's names. Japanese-speakers tend to consider -ko (meaning "child") to be a feminine ending. The name "Dagmar" might make Americans imagine some kind of high fantasy warlord king, but it is in fact a Germanic girls' name. (For more on coming up with SF names, check out Tricks & Tips For Creating Fantasy, Sci-Fi, & Other SF Names.)
If you look up the meanings of various names, you'll find that many girls' names refer to purity, beauty, gentility, or a flower. Boys' names often refer to rulership, animals, locations, or an occupation. Of course, a speculative fiction culture might be much more egalitarian, or they might have somewhat different ideas of what are proper names for males and females. (If they have males and females at all, anyway.) If you take the time to develop languages and a linguistic history for your cultures, you can choose likely names based on the meanings of words.
Finally, you can try out the random name generators. There's most likely a name generator appropriate for the type of character you want to name.