Romanization from Japanese to English does have some standard systems, but it isn't itself "standardized" entirely, and as such there are going to be discrepancies.
Most romanization is based on the Hepburn system and its many variants, which does use "ō" to denote the "おう" sound (except if there is a word border between them, or if it's being used for the "ou" form of a verb).
Japan also has it's own "Nippon-shiki" romanization style which is mostly pretty archaic at this point but I still come across it. It's based more on telling you what characters were used in the original Japanese, not how they actually sound, so as a result many automated kana-to-romaji systems use it. It also uses a circumflex instead of a macron like the Hepburn system in order to indicate long vowels. In Nippon-shiki, しゅぎょう would be romanized as "syugyô."
The Passport Standard of romanization, is permissive for the sake of names. So the names Itō, Itou, Ito, and Itoh could all be the same name, just romanized differently. Admittedly, this does result in some confusion (大野 means "big field" and 小野 means "little field," so they're complete opposites, but with passport romanization they could both be spelled "Ono"), but with personal names it doesn't matter as much.
When it comes to artist names (and other proper nouns like song titles), what system is used amounts to little more than a stylistic or marketing choice. Sometimes a name just looks cooler with two i's instead of one, or with an h instead of a u, or whatever. In English, the length of a sound isn't a phoneme that makes a difference in meaning, so in order to further "anglicize" words, Japanese writers and artists and professionals will often omit sound lengthening notation entirely, rather than choosing between one.
Take 椎名林檎 for instance, whose name has been romanized at least 3 different ways in an official capacity: Ringo Sheena, Shéna Ringö, her website currently spells it as Shiina Ringo, etc. In her case, those first two aren't real "romanizations" so much as they're deliberately written to say "I'm a rock musician" ("Sheena" is probably a reference to the song "Sheena Is A Punk Rocker" by The Ramones, a reference invoked by late 70s female-fronted japanese rock band Sheena & the Rokkets; the umlaut over the o in Shéna Ringö is just a really common metal trope). Again, style over "proper" romaji. It's not just her either... for example, B'z lead vocalist 稲葉浩志 was once constantly credited as "Kohshi Inaba" but is now "Koshi Inaba" despite the official romaji of his name being "Inaba Kōshi."
So yeah I guess Ayu just stylistically decided the song should be called "Load of the SHUGYO" rather than "Load of the SHUGYOU" or "SHUGYOH" or anything... just... because! lol
