their way rather than how they should be.

Every language has different sounds. It has long been understood that languages will translate words/names into versions they can actually hear and pronounce. Sadly, some people mock or demean people who try to speak a non-native language and make errors in it. In the U.S. it used to be fairly common to mock Asians coming from a language with only one liquid consonant sound for their inability to differentiate between 'r' and 'l' sounds.

I know I can't hear the difference in various Russian language vowels and while I can hear tones, I don't know how I'd explain their pronunciation in an Anglicized name -- or if it would be relevant.

While I appreciate that regional accents mean that non-U.S. citizens might not say "comma" the way it is heard in the U.S., I do expect that if a U.S. citizen tells me to pronounce their own name in a U.S. manner, then that is how it "should be" pronounced.