[chryuop]

So you decided to change your name. You do it and change it into a foreign language you don't know and pick a random word whose meaning you ignore.

That beats by far people coming in here asking for a tattoo word. As per how to write it, what does it matter? You are not Japanese nor speak it. I didn't understand if you live in Japan (but I doubt it), so spell it the way you like and pass it for Yuki.
(And why did you use Yukiko as a screen name?)