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.
If you can treat the gendered name simply as a grammatical construct, things are easy - and a "name" like "Elena Kuznetsov" would simply be a grammatical error and never occur as a real name.
However, now people from abroad visit the country or possibly even (re-)immigrate and suddenly you do have real-live "Elena Kuznetsovs" - in addition to the regular gendered names. This sounds pretty complicated to keep track of.
Coincidentally, this actually makes it possible to have names that don't conform to the standard gender patterns without much confusion, because as soon as you start talking about what the person is like or what they're doing, you have to specify the gender anyway, so the marker on the noun is mostly redundant.
But also Russia in particular has a long-standing cultural tradition of Russifying foreign names of immigrants. For example, Americans don't have patronymics, but when you get Russian citizenship, they will ask you for the name of your father and assign one accordingly - so e.g. John, son of Donald, would become Джон Дональдович. Similarly last names are often modified by appending -ов or -eв, although this is less common today. Anyway, a name of clearly Slavic origin like "Elena Kuznetsov" would almost certainly be nativized if that person immigrate.
This usually doesn't apply to non-immigrants, though. Thus e.g. Barbara Liskov is still Барбара Лисков in Russian, not Лискова. Which makes it very confusing when a native speaker first sees the last name and confidently decides that it's male.
There are also some weird cases where names with obvious Slavic patterns are not re-nativized for political reasons. For example, Isaac Asimov is originally Исаак Озимов, which has very clear markers of a Russian Jewish name. When his stories were translated to Russian in late Soviet era, though, his name was rendered as Айзек Азимов (i.e. a direct transliteration of English), and it's been said that this was a conscious choice by translators because that way it didn't sound Jewish, which helped get it past censors when "anti-Zionism" was particularly prevalent in USSR.