Why is it that Neptune's name is written as ネプテューヌ and not ネプチュヌ? The title of Hyperdimension Neptunia game in Japanese is written as . My question is, why Neptune is written as such? Shouldn't the "tu" in Neptune be be written as "tyu" 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 ) form is just "artistic freedom" IMO.