The title of Hyperdimension Neptunia game in Japanese is written as 超次元ゲイム ネプテューヌ. My question is, why Neptune is written as such? Shouldn't the "tu" in Neptune be be written as "tyu" （チュ）since it is read as Ne-pu-tyu-nu?
Simply the stylistic choice to use a variant pronunciation. [tju], [tʃu], and [tu] are all allophones in English. Japanese typically uses [t͡ɕu] (close to [tʃu]) for Neptune because it's the closest match to the native phonological "rules". This atypical (much more so than トゥ) form is just "artistic freedom" IMO.