I've done an original character based on an existing design and universe, for entirely practical reasons. I knew that if I dressed as Neytiri or Grace from Avatar I would drive myself crazy trying to recreate their exact stripe patterns. That didn't sound like fun, so instead I invented another AVTR driver scientist and yes, gave her a name and a bit of backstory. I still call it a recreation costume, though.
I've got nothing but respect for people who design original costumes from scratch. My brain just doesn't do that.