I don't really have a system when it comes to choosing the the perfect name for each of the characters in my stories. The name I spend the most time deciding upon is my main character's name. Since I'm going to be spending a lot of time with them I really want to love their name and not despise it whenever it comes up, or else I might start hating the character all together. For other characters I pretty much just pick whatever name I can think of really, I'm not very picky when it comes to them, plus I know I can change names later on in future drafts if I want to.
For me, finding the perfect names for my characters is one of my favorite parts of the writing process (and a also a great way to procrastinate, lol)! Two of the websites I like to use when I'm on the hunt for the perfect name are Baby Names and Nymbler. They're simple and easy to use and have a ton of great name suggestions along with name meanings and other interesting information!
Some of my favorite character names from books are names that reveal a lot about the character themselves. Some great examples of this are: Scarlett and Rosie March from Sisters Red by Jackson Pearce, Ethan Wate from Beautiful Creatures by Kamie Garcia and Margaret Stohl, and, of course, all the character names from the Harry Potter series by J.K. Rowling! All of her character names are as unique and awesome as the characters behind them (I'm looking at you, Dumbledor, aka bumblebee! :))
Happy name hunting!