I have a German coworker named Martin. He, of course, pronounces his name the German way: "MAHR-tin". Every other person in my group speaks either Chinese or Korean as a first language, and they all call him "Ma-teen". I realized today that when I talk about him to, say, my husband the native English speaker, I pronounce his name in the distinctly American way, "Mart'n". But when I address him to his face, or refer to him among my Asian colleagues, I enunciate the second syllable the way they do, "Mar-tin".
I have a similar dilemma with a fellow volunteer at Rotacare, the clinic where I volunteer as a Spanish interpreter. Her name is Diana, which in her native Romanian is pronounced "Dee-AH-na". Of course, we English speakers read her name tag and think "Dye-ANN-a". She's emphasized that either is fine to her. I find that what I call her depends on the last language I've been speaking. If it's English, I'll pronounce her name the English (American) way, but if my brain is in Spanish mode, I'll pronounce it as it would be done in Spanish, which is essentially the same as it is in Romanian---the languages are quite linguistically similar.
I suppose the polite thing to do is to honor the wishes of the person you're addressing. Most people I've met seem to accept whatever pronunciation is natural for the speaker. My own first name is Karin, which I pronounce the same way as the more commonly spelled Karen. Nevertheless, when I was in Germany, where my spelling is the popular one, I was quite happy to answer to "KAHR-een". But I once heard of a Latina woman named Miriam who hated the Americanized "MEER-ee-um" so much that she instructed her American acquaintances just to call her "Medium"! Indeed, that's a much closer approximation.