Well the original fanfiction "Masters of the Universe" actually used the original character names Bella, Edward etc. The author scrubbed the Twilight names off herself and renamed them Anastasia and whatever and was then selling them as self-published books "Shades of Grey" and the other two via the
Amazon self-publishing platform.
She also had quite a marketing campaign going via various blogs and message boards geared toward the romance/erotica readers. Seriously, these were one of the most heavily word of mouth promoted self-published books I've ever seen. There was a huge amount of fuss over how she was "spamming" boards and getting her friends and fans to do the same. It was like a drama a week over these books. It all kind of went viral and
then Random House picked up the publishing rights and reissued her self-published version under their imprint. Random House has stated that the books are original enough not to violate any copyright issues but when the blog Dear Author ran it through the software college professors use to check for plagerism, they found an 89% match rate of Shades of Grey to Masters of the Universe.
I'm not convinced yet that Stephanie Meyer won't have some sort of legal response because the ties of the book to Twilight are quite clear. It would be an interesting case.