Actually, while Dothraki doesn't, some languages just put everything through their inflection pattern. In my native language, Finnish, any foreign noun, name or what ever, is inflected (when not in nominative), otherwise they can't really be used (when a case other than nominative is needed). It can be awkward, when the phonemes or intonation are different, and in some rare occurences, our intuition on how to inflect unfamiliar words may even falther, but we do it anyway.
In Dothraki, native names like any other native words can be inflected, so "Then head of Drogo" should be nhare Drogosoon, if I'm not entirely mistaken. AFAIK all human names should be animate. I'm not sure, how animacy of names would go for, say cities or countries, all animate I'd guess.
With un-assimilated foreign words like foreign names, Dothraki uses a specific method to exclude them from the inflectional (as well as prepositional) syntax. When any other case than nominative is needed, they put haji in front of the word and then just don't inflect. And you need to get from the context, in what sense the foreign name is used.
The head of John is thick. -> Nhare haji John nroja.
The clothes of John are thick. -> Khogar haji John nroja.
The head of Drogo is thick. -> Nhare Drogosoon nroja.
The clothes of Drogo are thick. -> Khogar Drogosi nroja.
