Trying to write Japanese words in English letters is called romanization, and there's several systems for it. Most common being Hepburn.
Wiki page for more than you ever wanted to know on the subject.Basically, in Japanese there's more or less four different ways to write an O sound:
お (o)
おお (oo)
おう (ou)
おー (o with an extender)
The first is a shorter sound, while the latter three are longer and all pronounced pretty much the same (though show up in different words). As a result, many romanization systems lump the long o's together as "ō" or some variation, differentiating them from the shorter "o". Alternatively, you can stick closer to the Japanese spelling and use "ou" "oo" etc. which is also valid. Using "oh" instead is also valid, though I find it really annoying.
Sometimes "ou" is written as a plain "o" but then you're losing a bit of information.
In the case of Touhou, it would be written in Japanese as とうほう (to-u-ho-u) so Touhou would be my preferred romanization, though "Tōhō" would technically be valid. You could use "Toho" and it would get the idea across but it would be kind of strange. That said, the Japanese film company "Toho" is actually spelled the same way as the game series, ignoring Kanji. Probably because they chose their official romanization when things were less standardized, I guess.
Edit: Just to further clarify, by "long o" and "short o" I don't mean what that typically means in English. They're all pronounced "oh" in Japanese. I'm talking about the length of the sound in the literal sense. Like "oh" versus "ohh". Vowel-sound-length is an important thing in Japanese. Get it wrong and you end up with a completely different word.