I'm a CIT at a Girl Scout camp so I understand what you are going though right now trying to come up with a camp name, I finally ended up being Olive and I love my camp name. I have never heard that you are not supposed to make up your own name, I was given mine but I know people that came up with their own.
Here are questions to ask yourself when coming up with a camp name:
What is my favorite ______? (fill in the blank; movie, tv show, book, animal)
What is a place I really like?
What nicknames did I have when I was little?
What is my personality like? (I definitely have a friend who's camp name is Spaz because she is a spaz)
What are my pets name?
What do I like?
What sport do I play? (If you swim how about Speedo or Dolphin, if you play basketball what about Hoops or Dunk- master)
When I grow up, I want to be a ________?
Do I speak another language? If I do, what are some really cool sounding (but easy to say) words in that language?
What games do I like to play in my spare time?
Also ask friends and family if they can help you come up with a camp name. Have them ask you questions. It may take a long time to come up with one but that is good because you are kind of stuck with your camp name for a long time.
Hope that helps!