In Yu-Gi-Oh is Bakura's first name spelled Ryou or Ryo since the manga says Ryo but the spelling accepted and used everywhere is Ryou?

Answer 1

His name in Japanese is transcribed to Ryō in Western characters, the symbol over the o indicates a long consonant.

Because English is not a phonetic language though, you can render Japanese words like that in different ways, all of which are technically correct. 'Ryou' is valid, and probably the most common way of writing an expanded long 'o'. But Ryo is valid too, as in English, the 'o' can be short or long without using accents, umlauts or dipthongs.

The deciding factor is picking the form that an English speaker is most likely to pronounce correctly. The long 'o' in 'Ryō' is pronounced like the 'o' in 'bowl', and most English speakers would pronounce 'Ryo' that way too. On the other hand, many English speakers would see 'Ryou' as bring pronounced it 'Ree-yew', due to having the 'you' in it. That'd be the correct pronunciation for a different name, Ryu.

So as an answer, if you were writing in 'romanised' Japanese (Japanese in western characters), you would write it as Ryō or expand it to Ryou. But if you were using it in text translated into English, 'Ryo' would be the better choice.