At first I desperately wanted to keep my initials, and after perusing some sites which listed the popularity of names by birth year, I came down to Cassandra March, then Cathleen March, and after a while I decided I didn't like that name at all. Whenever I said it, it wasn't me.
Since I'm both Irish and Danish, I decided I wanted an Irish first name, and I came across Shannon (i.e. the Shannon River). There were a couple of girls at my high school named Shannon, so it's not a terribly out of place name, and I decided I wanted my mother's maiden name as my last. It's a wonderfully long, convoluted, and hard to spell Danish name and I just adore it. It took me until I was about 8 to learn how to pronounce it correctly. 😀