It's too bad that Harry LeBlanc doesn't post much to this blog, because in his unpublished novel Tainted Cotillion, every character's name is significant in some way, from the protagonist (Toussaint, named for the leader of the Haitian revolution) to the chief villain (Camille, named for the hurricane -- the book is set in New Orleans). None of my names are that significant, but I do tend to think pretty carefully about naming.
First, I want the names to be ethnically consistent and historically plausible. My first novel was set in an alternate Italy, so all the names had to at least sound Italian. During one of my revision passes, a beta reader pointed out to me that many of these characters were named after Christian saints in a world where Christianity had followed a very different course. He suggested The Lives of the Later Caesers as a source for late Roman names. Conveniently, I actually had that on the shelf. (My husband was a History major.) I made a list, and then went through and vetted every name. One I specifically remember changing was Francesca, who became Flavia. The name Francesca is based on Francesco, and became popular because of St. Francis of Assisi. It actually means "French." It's not entirely implausible as an Italian name absent St. Francis, but I wasn't tremendously attached to the name, so I changed it to a solidly late-Roman one. One I kept anyway was Giovanni -- Giovanni is the Italian form of John. I had reached the point where I couldn't conceive of that character by any other name -- he HAD to be Giovanni.
Second, I want the names to be distinct and easy to tell apart. One of my rules of thumb is that no secondary characters can have names that could be easily confused with a primary character. So, Eliana is the only character with an E name in my first two novels (unless I missed one). Lauria is the only one with an L name. In real life, it's pretty common for people to run into people with the same name, but in my books, it never happens because it's confusing to the reader.
Third, I want the names (at least of protagonists and other major characters) to have a sound I like. I really like the names Eliana and Mira. I really like the names Lauria and Tamar.
Fourth, if the name tells you a little something about the character, that's a bonus. In my newest novel, I have a character named Heike, which is a pet form of a female form of the German form of the name Henry. Which means "home power," and is significant in the book. (OK, so that's not going to tell very many people anything about the character unless they look the name up in a name dictionary, but oh well.)
For my current project (a children's SF novel) I gave the two girls in the story my daughters' middle names, Jean and Margaret. The boy in the story was named after Robby Smart, the most annoying boy in the fourth grade. (Robby grew up to become a sculptor and I would expect is much improved. But he was pretty awful when he was nine.) Eleanor complained about the whiteness of the names. I haven't changed them, but I've been mulling over whether I will do so later and if so, what I'm going to change them to.