Kitsune is the Japanese word for "fox". Foxes are generally regarded as mischievous enchanted animals capable of transforming themselves into human shape and engaging in also sorts of mischief while doing so. Foxes in some repsect play a similar role in Japanese folk belief as do witches and elves in English folk belief. There have even been "fox trials" of accused foxes. We haven't found any examples of the name "kitsune" in medieval Japan and we don't think it would have been used as a name.
Names of animial have been used to form personal names in Japan since the Heian period. Generally, people have prefered to pick the names of auspicious animals such as "dragon" and "tiger," both of which are part of the Chinese zodiac.
If you would like a name which sounds similar to "Kitsune," you could use "Kitsume," which is found as early as 793. (1)
Solveig Throndarsdottir researched this letter.
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Academy of S. Gabriel
(1) Nostrand, B. "Name Construction in Medieval Japan."