One thing that I am obsessed over when planning a new story is names. So much goes behind a character's name. I once had to rename a character because the name that I originally gave her was hindering me from delving deeper into her character. Once I changed it, her personality came much more freely to me. It was pretty crazy.
I love finding meanings behind names when I read, and so if possible, I like my characters to have names with hidden meanings as well. It doesn't always work that way, of course. Sometimes a character just is Mary or Justin or Alex, for no particular reason. And minor characters tend to have less of importance to me when it comes to deeper meanings.
When I was younger I used to flip through the name book my parents bought in 1986 for their first child.
But as I got older and internet became more popular and my parents let me use it, I've found two sources that are gold in finding new names. The first is babynamesworld.com. It's just a great place to browse, and their searches are crazy good. You can choose the sex, syllables, letters, origin, and meaning all in one. It's great. The second website that I've more recently found is behindthename.com. This goes into more of the historical/mythological/literary/Bibical aspects of some names. It's handy if you want a bigger meaning behind your character's name.