When I was a whole lot younger, I found this book of my parents, how to name a baby. When I was in search for a name for a character, I would search the contents for the meaning of a name, thinking I could mold the character to it's name. It doesn't really work that way. These days, I tend to create the personality first, than go in search of a name. It has to fit, give off a vibe that it's right. Friendly girl, a friendly sounding name; saucy woman, saucy name; a tough guy, a tough name. That's not exactly symbolism, because you're still the one choosing them. What you think fits with this exact character.
I mostly write fantasy, and so name generators can be a life saver. Normally I try to stick with names to fit the race and personality. For example, if I were to have an orc warrior, who had more brawn than brain, I'd name him something rough and tough sounding, like Kurtek, Krunk, Glurbash, etc. But if I had a human aristocrat with a knack for getting himself into bad situations, and talking himself out, I'd name him something more flowing and fancy sounding, like Cacius Valius. As far as symbolism goes, I personally try to stay away from it, just because I don't find it realistic. My name, for example, means Pearl and Fire, though nothing I've done, or ever plan on doing relates to that in the least. I've only used symbolism a handful of times, and I never really stick to those characters, because the name could sound cheesy, or it just doesn't fit that character. I personally tend to stick more to the sound of the name, not the meaning.
I go for symbolism and use the names of stars which are mostly in latin and arabic, others I try to find names that go with their appearance or because they are clever (one of my characters can manipulate gravity so I call him "Newton")
I recently discovered how useful a name generator can be.
I often use symbolism when naming my characters. I'll often name them after someone or something. My username, which is also the name of one of my protagonists, is a combination of two Greek words: "peripateo" which means to walk, and "abyss-" which is the root form of "abussos."
I usually try to find a name that suits that character's personality or something that suits they way she looks, acts, where she lives, what age it's set, etc. When I'm naming a character I usually spend a lot of time on baby name sites. ^^
Carl's guide to naming characters: 1. Have you decided on a name? Yes: Well done. No: Go to step 2. 2: Go to a babynames website the sorts names by gender and first letter. 3: Filter by the gender of your character (unless you specifically want the opposite gender name. See: Scrubs) 4: Pick a letter that you happen to think sounds good, today. 5: Pick a name you like. Is that name likely to be given to your character, given culture, setting etc? Yes: Go to step 7. No: Go to step 6. 6: Does that matter? Yes: Go to step 5. No: Go to step 7. 7: Congratulations, you have named your character. Repeat for other characters or move on to actual writing.