You might at least be able to find a name that is easily pronounced in both languages. For example I have a friend called Pavit, which is not an english name. But is nevertheless easy for english people to say.
I'm English but learning Hindi, so I know to pronounce it 'puh-vit' as it were, but 'naturally' (or however many years since I started learning ago) I would read/say it like पैवित almost, you know, short English 'a'.
The word is obviously foreign, so a lot of people wouldn't even consider applying that style of pronunciation.
The standard way to pronounce "a" in foreign words is as in "father". But this one makes me curious; Hindi is like English in that a written "a" is often pronounced reduced. (Compare the traditional spelling suttee to the "reformed" spelling sati, which more closely reflects the Devanagari spelling, or the spelling of the English word "jungle" to the Hindi word of the same pronunciation, jangal.)
So it's possible that a highly nativized pronunciation of "Pavit", if stressed on the second syllable, might be correct!