Just a question that's been bugging me for a while, what are the correct way
to spell some of the names?

Ukyou or Ukyo?
Ryouga or Ryoga?
Kunou or Kuno?

also:

Mokou-Takabisha, Moukou-Takibisha or Mouko-Takabisha?

Hiryuu-Kouurin Dan, Hiryu-Kuurin Dan, Hiryuu-Shoten-Kuurin Dan, Hiryu-Kourin
Dan?

Confusing ne? ;)

      K  u  s  a  n  a  g  i       K y o
      --|---|--    --|---|--     ----+----
       +-----+     /-, +-+-       +-----+
       |-----|      |  |-|-       |     |      
       +-----+     -|- |-|-       +-----+
      ----|----    / \ +-+-       /  J  \
 -----------------------------------------------
  "Kusanagi Flames, Yagami Tears, Orochi Blood"