User blog comment:Mckrongs/Monster Hunter 4 for the Nintendo 3DS/@comment-7264921-20130926121058

So, there seem to be some doubts concerning Amadyura's name, or other japanese words containing this type of yōon (デュ、ディ、 etc). And it's understandable, because if you type "dhu" using a japanese IME (Input Method), you actually get デュ.

But "dhu" isn't the proper romanization of デュ in the Hepburn, the Nihon-Shiki or the Kunrei-Shiki systems (the most used romanization systems). "Dhu" is a short input for デュ using the IME. Other ways of typing デュ are "delyu" (de + litte yu) and "dexyu". Note that "dhu" is way shorter than "delyu" or "dexyu".

Considering we use the Hepburn romanization here (which is the most used system in the world), I suggest we stick to its chart and romanize デュ as "dyu", ティ as "ti", and so on.

Sources:

http://en.wikipedia.org/wiki/Hepburn_romanization#Hepburn_romanization_charts

http://www.loc.gov/catdir/cpso/romanization/japanese.pdf