Mostly (for me) naming characters it is a bit like naming a baby or a puppy: you try to go with something fairly normal so they won't get beat up in the playground or sneered at while you're walking them in the park. And something nice. Something that suits them. So there's the Baby Names approach.
There's also the Dropping Hints approach. For instance, a character called Thomas Lynn is going to make me hold onto everything and wait for the Queen of Fairies to arrive. A girl called Ella mistreated by her family causes me to be on the lookout for fancy but fragile footwear.
These are the fairly unsubtle Dropping Hints names. There are also very cool Dropping Hints names. In Diana Wynne Jones's Howl's Moving Castle the wizard Howl is actually named Howell Jenkins, which tells us about his super-ordinary Welsh background, about the name he's chosen and how he wants to appear to people, the kind of person he is. About the name he hasn't chosen.
Those names are my favourite kinds of names. There's a girl in Demon's Lexicon called Mae, and she introduces herself by saying 'not like the month, like Mae West.' Which isn't just about spelling, of course.
We use names to make ourselves seem the way we want to be, and when we're making people up their names are important! They're our best label. (Plus, Mae West is really awesome. Everybody knows.)
There's also Naming Characters After People. I don't use real people's characters in my books (because they would yell, and sue me) but sometimes I do just need a name, any name! And then I pick one of my friend's names.
So one day the beautiful and talented Susan (one of the many beautiful talented people I have so unwisely chosen to associate with), my writing buddy in Ireland, veteran of many days in cafes with molten lava cakes and my friend since I was sixteen, said unto me accusingly: "You've never used my name in a story."
"No?" I said, a little startled. "Okay, well, I will!"
Some months later Susan called me.
SUSAN: So I was reading your story. And there was a Susan in it, all sexy, and much with the making out, just like me. And I was so pleased.
SUSAN: And then she turned out to be a transvestite explain yourself.
SARAH: Um. Um. Coincidence?
Speaking of Susan, she just scored her first book deal. If you guys would go congratulate her, that would make me very happy! (And might make up for the, uh, transvestite thing.)
Another instance of this is that I used the Durham Lass's real name in my book. And in my first draft, I killed her. She took this surprisingly well, and even agreed to move in with me.
My agent, however, was very set on saving the Durham Lass's namesake. And she was right, too, but we went back and forth on it a bit. There were several days which I spent pacing the floor fixing people with a beady eye and announcing darkly: "I must kill the Durham Lass. I must have blood."
The Durham Lass did not move out. I can only attribute this to an act of God.
So, how do you name yours?