Alternatively, what do you expect or find most agreeable for visitors from other countries to do about names you can't pronounce?
As a US English-speaker, I generally try to learn how to pronounce a name as close to the way it would be pronounced in the original language. To me, this is a sign of even nominal respect, although I also expect to have mistakes forgiven without a to-do. I have frequently been baffled by people who tell me that it doesn't matter. I had a friend in high school whose family was Indian, and whose name was Yamini. Everyone in school called her ya-MEE-nee for as long as I can remember. After we had finished school, I came to learn that in her family/language, it was YA-mi-ni. I berated her for not telling us we were mangling her name all those years, and she really seemed puzzled. A couple years ago, the department where I was working as an admin hired a visiting faculty member whose last name was Nguyen. When I met him, I greeted him politely, shook hands, and said straight-forwardly, "Now, tell me how to say your last name." I'd seen it written several times, but not, to my knowledge, spoken. His response took me aback completely, because he said diffidently, "Well, *I* say 'nwen.'" Still, I continue trying to get "correct" pronunciations.
What I was taught about Japanese is that, especially for given names, one just imports the name, spells it as well as possible in katakana, and people will pronounce it the way it's written. No idea how well that reflects reality, or what one should do with family names. The one time I tried coming up with kanji that was a literal translation of my family name and suggesting to a Japanese friend that I could use that as my family name 'in Japanese,' she got a very peculiar expression on her face, and I hastily retracted the proposal before she had to figure out a polite response.
When I was studying French, in school, it was expected that I answer to a reasonably French name. Since my first name had no equivalent and was unpronounceable, I went with the French pronunciation of my middle name. But whether that reflects anything to do with French attitudes toward names or was just a pedagogical tool, I have no idea.
Now I'm considering 'my name' in Spanish. If I go to a Latin American country and want to introduce myself, should I
A. Break a Spanish sentence with my name pronounced exactly the way I would when speaking English?
B. Pronounce my name with the closest equivalent available in Spanish phonemes?
C. Translate my name, which is a common as well as proper noun, and use the translation - which means the same thing but has no sounds in common with my name in English, and may not be a generally recognizable given name in Spanish?
D. Pick a recognizable Spanish name which sounds sort of like my name in English?
What's funny is realizing that I appear to have a powerful double-standard: option A feels really wrong to me, and yet is essentially what I expect and appreciate from others bringing their names from their language into English.
And - last question - if I go with option C, what do I do about the fact that I'm female, but the common noun which is the translation of my name is masculine?