In my experience, the name just gets converted to whatever is the closest equivalent in the target language. Or gets horribly mangled if the two languages are different in phonetics and syllable repertoire, which they usually are.
Yep which is why it's the smart play to make the spelling in the target language just whatever will make a speaker of said target language say it right.
I've always considered my name to be the sound, the spelling is just an implementation detail.
