I noticed that you can't use titles, like Mr.
There's a profanity filter, so you can't actually name a pet Nuts.
There's a restricted list, but that can't be comprehensive, so the more popular religious and copyrighted names can't be used, but less common names can be.
As far as I can tell, the restrictions are similar to (if not the same as) character naming rules.
On a side note, I don't think Simba can be copywritten, since that's an extremely common name for a lion that you see/hear in old movies and other sources. Of course, it's been extremely popularized by Disney, but it's the word that means lion in Swahili. I wouldn't expect that Disney could copywrite words in other languages, especially common use words/names. It would be like someone copywriting Leo. Of course, I could be wrong and the courts/government could be just that stupid.