@tsarstepan,
No, I don't care. I think people take their names much too seriously. My last name is easy to pronounce but it's spelled weirdly so I'm used to people screwing it up. I don't even bother to correct them unless they specifically ask if they've pronounced it the way I pronounce it. I don't care if people screw up my first name; it's just not that important. If someone asks me what my name is I'll tell them but "Hey you" works great.
I got a lot of downvotes on an A2K thread for suggesting that people are under no obligation to attempt to pronounce a foreigner's name the way it's pronounced in their native country, especially when the name is distinguished by subtle accents, as you point out, or diphthongs not found in English. I was playing with a Russian pianist once whose name was Dzhordzh. I couldn't pronounce it and he just smiled and said, "Call me "George". He was tired of people trying to be polite and mangling his name in the attempt.