A double name opens you up to lots of nicknames. I had several growing up thanks to a set of friends obsessed with calling each other by any name other than her own. (Shout out to my homies DiDi, Ro, Ames, Peen, Ash and LinMayn!)
Nicknames are probably especially popular among tweens and teens. It could be a good writing excercise, particularly for a YA author, to think about a character's nickname, or what it would be if she had one, and why. You get into who she is, and the dynamics of her social circle.
Lottie, my protag, doesn't really have any nicknames (except that Lottie is short for Charlotte).
So instead, because I shamelessly enjoy talking about myself, I'll just give you my own. Each of these was cross-my-heart used by my friends while we were growing up:
AC Slater. One of the most popular. We'd seen every episode of Saved By the Bell (who hasn't?) and I thought that's how high school really was. Until I got there, that is.
Air Conditioner. Because of my initials? Get it?? Hahahaha...ha...ha...
Claris Works. This one is from elementary school. It was a typing program we used in computer class. I just found it on the internet but it's so old-school it doesn't even get its own Wiki page.
Cenna Stampys or just Cenna. In ninth grade we got t-shirts made for Key Club with all the members' names on the back. When the shirts came in, we couldn't find my name on it. Then we saw Cenna Stampys and figured that had to be it because nobody in our school was named that. Instead of me being listed as Anna Claire Stamps (maiden name) or even Anna Stamps, somehow somebody's handwriting sucked and the printer just guessed and that was what he came up with. That's my theory, anyway. My sister says she's going to have her future children call me Aunt Cenna because Aunt Anna Claire just sounds awkward.
Deaf Girl. The most un-PC nickname. I got this one from my habit of talking with my hands (and thus looking like I'm using sign language.) Also from not paying attention when someone was calling my name. Although honestly with this many names, that was probably inevitable.