I tend to name my characters early on in the development process. Often, the name is so wrapped up in who my people are that I can't imagine them being called anything else. When an author assigns a name to a character, we latch onto it and begin to associate all kinds of meanings with that name.
For example: Jason Bourne
For those of us who have seen the Bourne movies, instantly we've got a plethora of words pop into our heads-- action, intensity, running, danger, intelligence, shooting, memory loss, intrigue.
Now let's analyze him a bit more, starting with the name Jason - This harkens way back to the mythological hero Jason and the Argonauts, searching for the Golden Fleece, traveling the world, battling evil. But the name also surprisingly means "healer." Interesting.
And then there's Bourne - This brings to mind rebirth, new life, bearing weight, and second chances. Put the two names together and you get someone who's fast, cool, yet has a subtle compassion about him. But that's not it! You see, Jason Bourne is not his real name... he's actually David Webb - an ordinary citizen who was trapped in the web of a secret CIA operation.
The key is not to come up with some witty, telling name (like Boris Badenov), or a cliché symbolic name (like Raven), or a name that just describes their appearance (like naming someone Ebony because they have black hair). Instead, take it a step deeper and find ways to evoke certain feelings about your character with a subtle name that represents the heart of your character well. One writer who I think does a marvelous job with naming is Suzanne Collins in The Hunger Games: Katniss Everdeen, Prim, Haymitch, Effie Trinket, Gale, President Snow. Each unique name has so much life and meaning behind it, without being in-your-face obvious.
Right now I'm working on developing characters for a possible webcomic. The main character is a superhero, but she's also deeply troubled with multiple personality disorder (a result of the event that gave her superpowers), and she tries to cover up her fear and anger by becoming goth. I've decided to name her Sydney. Without giving too much away, she's edgy and modern, and now that she's goth, she goes by Syd.
So, one last thought: Why do you think God left it up to Adam to name the creatures of the earth? Why do they need names? Why didn't God just name them himself? What is so important about the names we assign to things?