I manually search for a name. I hate generators. Personally, I think even a character name should hold meaning. I often try to match up name meanings with the character's personality or maybe something that reflects their history.
Almost always, I create a character and then name them. This is probably because of my desire to make their name worth something.
But once in a while, I choose a name just because it sounds pretty or think it suits that character. I also not like limiting my characters to names based on gender. I have a male character named Cadence and another named Kaelyn. Cadence was named for meaning. Kaelyn was named because the name has French origins and I thought it sounded nice. Hiko was named using the characters for "hi (flame)" and "ko (little)" because the original Hiko was had fire element powers and I'm sure anyone who knows delinquent Hiko would agree that she's quite the spitfire. Also her hair is red :B
As for playing video games (because of the picture you have up there), I usually go crazy silly with names! XD When I play Dark Cloud, I name my party after Japanese musicians who share a likeness. When I play FFX or Pokemon, I like to name my characters silly things. I once had a Squirtle named "Swabs"... I don't even. I once named Tidus "Tight Ass" >_>;;;
Long story short: Naming my characters is usually the very last thing I do for them and most often their names hold meaning.
