First step. How strong is this character in the story? Is s/he a lead, minor (supporting) or incidental (casual walk-on type) individual?
Lead characters should have names that are easy to remember, be strong and fit the personality. Exactly what does that mean? Think of it as Mary Smith. Now exactly how exciting is that name? Does it bring images of adventure? Do you see her as a group leader? Is she the champion you want? Now think about the name Ellie McTaggarty. This names invokes a sense of strength, a leader, a woman who you probably don't want to mess with.
If you're writing a romance novel, your heart-throb lead could be George, Tom or Bob but Angus, Brock, and Caleb once more infuses your mind with a lead man with chiseled features and just the perfect amount of brawn to match the brain.
When you name your child, you agonize over making sure it is the perfect name for your child. So it should be for your story characters.
I wrote some detective mystery stories back when I first became serious about writing. My character? Jules Hamphert. What a great name for private eye - aloof, suave, catchy. I felt I'd created a name to match Agatha Christie's Hercule Poirot. Unfortunately, the story didn't match the character. I didn't realize that fact for several years. When I did, I changed the name and published the stories. But Jules Hamphert still holds a segment of my heart and I have him in a story more appropriate to his discipline. Yes, a mystery, but one that only Jules would lower himself to handle.
When writing Ancient Blood, my co-author agonized over the names, making sure they appropriately reflected the character, not only in culture, but also lifestyle. Yes, we created a history, a background life, for these characters since they will be repeated in the Ancient Blood series. We could have named our lead vampire "Ivan" which is a good Slavic name but "Ejup" added mystique and a hint of spice. As I originally wrote the first pass and being a typical Anglo-Saxon American, most of the names I used were very Anglicized. Jack Franklin, also an American, but living/working in Brazil, changed names to reflect the ambiance of the Amazon jungle. Queen Isa became Queen Itotia (eye-toe-chee-ya) and suddenly the story enshrouded itself in even more of the dark, forbidding, unknown Amazon jungle.
Minor characters also need to be named and appropriately. Don't cheat yourself, your readers or your character by tagging them with a wrong name. Imagine a Slavic priest with the name John Hanford? Step back. How about Bora Ianovic? How about a native Brazilian guide named Robert Sandini? Again, step back. How about Paulo Santos? Doesn't the second name bring a more vivid image to mind?
Now for those pesky characters who walk into the scene then disappear and well, maybe make one more appearance. Do you name them? That depends on what you want to do. You could name the butler, Hyde or - please don't - Jeeves. It adds a little atmosphere but really doesn't promote the story. Or have a name for your favorite diner waitress, Rita or Rose but it is not really necessary. So you can give a name to these ambiguous characters, like the butler who may be referred to several times but never really has a part in the tale. Don't dwell on too many trivial details about these characters. Remember, they are walk-on, walk-off. My friend calls these characters "pop ups" and seldom gives them a name. Telling the reader that Misty Roberts is wearing a camel-colored Chanel suit with pearl buttons is too much information. Especially if Misty's only reason to exist is to pass the note from Reggie to our heroine. Of course, you can give a little detail such as "Oh, here comes that snoopy neighbor's daughter." when Misty is spotted.
To keep things clear and focused, make up a chart or list of all the characters in your story, even the walk-ons. This will make sure you don't mis-queue somebody. I wrote a story with my lead's name as Mark, and then changed it to "Philip" and finally to "Noah." Imagine how confused I was during a read to stumble on Mark and Philip! I almost let it slip. I checked my cast sheet and discovered my error.
To make naming a tad easier, use baby name books. I have one for boys and one for girls - and they are very old. Today I usually jump on the internet and search since I can specify boy names and also include race or culture. No reason to search through six thousand names when you can shorten the list to those of Native American, Greek, or Brazilian heritage.