I don't know - some people just don't have a good ear for sounds. My mum continually does this to me and my kids. She really struggles to pronounce certain sounds.
Yes, I know people who either/or just can't mentally process/pronounce certain words or names. I don't know if there's something physiological about it or not, but to me, it seems to present as a verbal equivalent of dyslexia - which we don't generally try to shame people for having these days.
Of course, that might not be the friend's reason, but it is common - and not something that a lot of people can help.
If it is just a case of being lazy or stubbornly keeping it in her head that the name is A when it's actually B, then I agree you need to persist with her.
As for expecting people to use your own accent instead of their own when saying a name, though, how would people feel if they said every word in your accent when talking to you, instead of in their own? Wouldn't that just sound a tiny bit 'wrong' and possibly racist, depending on the circumstances?
Many English people just cannot pronounce a rhotic R - I believe it's something you frequently lose the ability for as a child, if the language you grow up speaking doesn't include it - any more than most of us could accurately make the 'clicking' sounds that feature in some African languages, or even some of the sounds in Dutch: when was the last time you ever heard a native English speaker pronounce Vincent Van Gogh's name correctly? Yes, he's long dead, so he isn't here to be personally offended; but it's the same principle.