Personally, I prefer the English pronounciation (or French...). I mean, when I write in English I'm supposed to use the Roman alphabet. I am also supposed to use the English grammar system. A sentence like "He's Janus, and this is Janus' cat" is possible in English, but a sentence like "He's Ianvm, and this is Iani cat" (or whatever) is not possible or would be very awkward. So, logically, I think I'm also supposed to use the English sound system (and alphabet system: J != I and U != V).
Actually, there's no major problem with Janus, but what if we're talking about Chinese names or names from other languages which use a totally different sound system than English (missing or additional phonemes, etc.)? Then it's even more acceptable and accepted to pronounce them in a way which is easy for English speakers. Sometimes, the custom goes as far as simply using another word which might not even exists in the original language: we speak about "China" and "India", never about "Zhongguo" and "Bharat" (or whatever the spellings are).
So that's for the historical names. For the names given to people, it's even more natural. In French, Achille is a name which is very rare but which exists. When some parents name their son Achille, I really doubt that they have the "Akhilleus" pronounciation in mind. They will rather think about the French pronounciation ("Asheel").
