Kunrei-shiki romanization (Momizi) makes sense to native Japanese speakers because it follows their phonological system. Hepburn romanization (Momiji) makes sense to English speakers because it gives us a better idea what things are supposed to sound like.
Or, basically, that syllable is a "zi" that sounds like a "ji".
"Fuziwara" is kinda silly, though, since it's switching romanizations in the middle of a name. But it doesn't really make much practical difference unless you're actually trying to make yourself understood in spoken Japanese. Personally, I've been trying to switch myself over to consistent romanizations for most names in Touhou... but I don't think I could ever get used to writing "Gensoukyou", so hey.