This is especially addressed to odyarb, who might have a better idea than the others how to answer this question.
How does one pronounce Genghis' names in Mongolian? Genghis is obviously not the closest transliteration, but how close is Chinggis? How about Temujin? The pinyinisation of that is Tiemuzhen, just as the pinyin for Genghis Khan is Chengjishi Han (I think). Using British English, or perhaps pinyin, what would be the closest trandliteration of his Mongolian names?