I need a good name for another character in my story: something unique and pretty like Clary or something like that... Can you help me? These are the names I have come up with: Hayden, Carly, Claire, Tessa, Jade, Alexis, Clara, Heaven, Ever and Serenity. Which one should I pick?

I personally like Serenity because it has a nice meaning that is unique and memorable. When finding a name for characters in a story, I find that it's best to not only make their name interesting, but also unbiased to a certain nationality/religion/group of people and not overly used. If the name is overly used, then people would have a tendency to associate other characters with the same name to yours. If it is really biased to a certain nationality/religion/group of people (unless you specified your character), then it kind of limits the reader's imagination on this.