The varied spelling probably comes from English speakers not hearing the subtle difference in sound in Russian.
The "I" tends to be a long "E" in English.
Here's another "Dmitri" (rhymes with "tree") Click "listen" after the speaker icon:
http://en.wikipedia.org/wiki/Dmitri_Mendeleev
The "Y" is more like "IJ", the "J" being soft, as in "bayou" or "yam".
Listen to the end of "Trotsky" (rhymes with "key") * :
http://en.wikipedia.org/wiki/Leon_Trotsky
Hard to explain without sound.
* some say "kee"