I'm jumping back in lol.
I pick names usually from baby name sites, or just names I like. Depending on the character, I'll go out of my way to find something that fits. Like in Undead, Riley got her name cause honestly I wanted something somewhat tomboyish, yet sounded journalistic lol. Her middle name came cause it sounds southern haha. But seriously, I could easily hear in my head "This is Riley Blake with the evening news..." lol.
Or in Divine Intervention, I just thought an Angel named Grace was a great fit. Plus for the time period she was in when she was alive, it's old fashioned enough to work. But usually it's just names I like.
My biggest pet peeve are names that are spelled just weird, like if you want to use a name, use the normal spelling! Don't use Safyre instead of Sapphire. Hell, don't use a gem name period LOL. I mean of course the irony of this is that I have what would be a Mary Sue name in a fanfic, but most people don't have names like that. Or when people use part of their names in every story. Like someone named "Katie" writes a story about a "Katrina", and then a "Kelly", and then a "Kristy", etc. It's like if you're doing a self-insert, be less obvious lol. One similar name can be a coincidence, several is just announcing it.