Giving your character the right name is essential, do take your time over this, its important, treat it as you would if you were naming a child. Does it fit? Is it suitable for the time period when your story is set, or where it takes place? No good calling her Kylie if she lives her life in 1920's England. Yet its okay to call her Elizabeth today, or anytime at all, and in any setting or genre.
Look for something unique to make your character stand apart. What about giving them a last name for their first name? Place names are good in this instance, how about Chester or Brighton? Add a surname from something everyday, like Friday maybe? Brighton Friday, or Chester Tuesday?
Watch the credits after a movie, or TV show and try switching different combinations of first and last names around. But do make sure you can pronounce the name you choose - readers don't like obscure names they can't decipher, or ones they falter over on every page.
What about Pitt Neeson, or Brad Liam? Not so good, maybe Ginger Day then? Or Doris Rodgers? See how much fun you can have brain storming a name for your character.
How do you come up with names?