I have a nasal vowel in my name that, so far in my life, only French and Portuguese speakers have pronounced properly.
I learned English in the US young enough that no one guesses I'm not native, and I anglicized my name so that it could be pronounced easily. It is what I go by.
I introduce myself with this adopted pronunciation. People often ask me how to pronounce it in French, so I tell them, but reiterate that I go by the anglicized pronunciation.
Inevitably, those folks start using their wrong attempt at French and I have to correct them and tell them I go by the anglicized pronunciation.
Edit: strong feelings had, obviously.
I will say though, I'm perfectly fine with people not being able to pronounce my name, and I do expect the same courtesy in return. I'll give it my best shot, but if it's not happening, it's just not happening.