Just to cover it: The ANN page for the series reads Kitsune, but is absolutely full with error-correction requests for character names, and for similar alternate-reading reasons.
That's her surname and first name by context and kanji reading. Google "羽衣さま" or "羽衣様" with quotes.
In addition, rendaku doesn't imply it's a single word, but rather is commonly seen in a single term - and even then you have many exceptions with rendaku, that have nothing to do with any rule whatsoever.