I've noticed something weird about the letter "O" when Japanese gets Romanized. I've noticed that sometimes the letter "o" is either an "o" or a "ou"...for instance I've seen the character Kyoka Jiro is either spelled that way OR Kyouka Jirou. Why do I see it spelled two different ways?

There are more than one way to romanise Japanese. In most all cases the short o is just o. The long ō can be ô using the Kunrei system but the more common Hepburn system uses oo, oh or ou depending on the subsystem used. o'o is used when the two o sounds are part of different syllables in the same word. On Gelbooru we always use o for short o and ou for long ō. The long ō is spoken about 1 and 1/2 times as long as the short o. It may not seem like much to us but it makes a big difference to native Japanese speakers.

More specifically:

traditional = The combination o + o is written oo if a word-border exists between them:
modified = The long vowel o is indicated by a macron ō

traditional = The combination o + u is written ou if a word-border exists between them or it is the end part of terminal form of a verb
modified = The long vowel o is indicated by a macron ō (You can see were the confusion comes in)

That and ō is not something most people can type on an English keyboard.

Thanks for the reply...

So the reason behind the "ou" is mostly concerning Japanese speakers? Do these o and ou differences matter that much to English-speakers? Seems like when I'm speaking English I've never had to worry about the length of time an "o" is held...only really the difference is between a hard "oh" sound and a long "oooo" is that the same thing?

I just find it weird because I had a discussion on the My Hero Academia wiki and they said the reason her name is spelled "Kyoka Jiro" because that's the official English translation by the company that handles that. Why wouldn't they use "Kyouka Jirou" if that is more correct?

The difference between o and ou is still there even if you're an English speaker. If you say an o too long or an ou too short, you might be saying an entirely different word (and the same with other double-vowels). A couple of examples using i and a instead of o are "oji-san" (uncle) / "ojii-san" (grandfather/old man) and "oba-san" (aunt) / "obaa-san" (grandmother). Or, for example, "oni" (demon) / "onii" (brother). If you're speaking a Japanese word that uses a double vowel, make sure to pronounce it longer.

The official English translation probably used Kyōka Jirō, but they replaced the ō with o to make it typeable on a standard US-English keyboard.