Hi fandom!
Kyuhyun's Chinese name is most assuredly 圭賢. SM Entertainment corroborates this in all of their printed, online, and DVD info. He has
written out his name in an interview. All those blinky flashy fan signs? 圭賢. 11,000,000 Google hits? 圭賢. I think we can be pretty sure that
that is his name.
圭賢 is pronounced "Gui1 Xian2"
100% of the time and the first character looks the same in both Simplified and Traditional Chinese.

His name is not, in any way, shape, or form, "Kuixian." This only works if his name is 奎賢 (Kui2 Xian2), which, if you will note in the image above, Kyuhyun thinks is wrong (this was an interview broadcast in Taiwan, and the mistake was only made once and only on this show). As evidenced by the adorable little "--X/圭--O" he's written next to it. and anyway, if you had to choose between having 圭 or 奎 in your name, 99.9% of people would choose 圭. Because 奎 is the obscure name of one of the stars that make up the Pisces constellation (alternately, quinine!). And 圭 is, you know,
jade.
If you want the "K" in there somewhere you want the Wade-Giles romanization (Kuihsien), which, by virtue of being the Wade-Giles romanization, makes no logical, linguistic, or common sense.
In conclusion, I submit that... I have no idea why the hell it is that fandom thinks Kyuhyun's Chinese name is "Kuixian." But I'm going to go eat jello now.
Yours,
Me.