So Russian families who move to America have a choice - either deal with people and systems who assume that married couples, and parents/children all have the same last name and hit roadblocks when that expectation does not match reality, or change one partner's last name to match the other's.
But that second option has problems too, because that name change doesn't retroactively apply in Russia - so now you might have American documents that say you're a Elena Kuznetsov, but your Russian documents say that you're Elena Kuznetsova - so any legal dealings that involve the two countries (like, say, traveling) become significantly more complicated because you need to prove that the two names actually point to the same person.
At least middle names aren't a big issue - patronymics mean something in Russia, but here in America it's just a string you pop into the "middle name" field, and maybe you get asked what it means, and get to teach someone what patronymic means.
Speaking as someone whose mom didn't change their name when marrying my dad, with a sister who didn't change her name when marrying my brother in law, with a wife who also didn't change her name when she married me, I think this problem is overblown. I have yet to encounter any actual issues with this.
Sometimes people will assume we aren't married and/or divorced, and people will often call me by my wife's last name and vice versa, but it has never caused any actual problem. Never had any system that assumes we have the same last name. So many people live in blended families anyway, that very few systems/people make these assumptions any more.
Nevertheless, the issue is real in the sense that many countries will e.g. "anglicize" your name when issueing you documentation, e.g. if your name includes characters they do not know how to handle. Having a single person with mismatching documentation _can_ cause issues. E.g. consider having two passports, with different names in them, and it's easy to see how this can cause problems.