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.
In fact, that's one way to guess/cold-read some information about a person. If you meet an Elena Kuznetsov in America, odds are pretty decent that she was born to Russian parents here.
They can exist, but sound weird in the language.
So now we have a few hundred thousand people with the last name Andersson, despite most of them not being Anders's son.
is a total non-issue. You can't, in any country I'm aware of, choose absolutely any name you want.
Want a name that is offensive in your language? Your country probably won't let you do that, but some other one might, and yours still needs to accept that name as valid.
You can't just go to another country and change your name there, but if you have dual citizenship, you can usually change it in either one, and the other one needs to respect that.
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.
For example, if you're male, and decide to change your name to Sarah, you totally can - but don't be surprised when people assume you're a woman.
And there are many countries, of which you are unaware, that do have pretty strict laws about what you are and aren't allowed to name your children. Iceland is the one that springs to mind off the top of my head. As I recall, Germany also has some limitations.
My point was governments do this all the time and it is a far cry from fascism. Elsewhere in the thread, it is mentioned that often times you have to compromise when registering a name in a different country (for instance, if the language does not contain a phoneme used in your name). In that case, you have to conform to the country's culture and language. Under that lens, banning names that violate cultural norms is not so crazy.
> You can't, in any country I'm aware of, choose absolutely any name you want.
Like in Germany can you name your kid "The Holocaust Didn't Happen"? No right?
Till the '90s at least there was an unofficial convention of anglicizing our surnames using the masculine form, ending up with things like Eleni (Helen) Papadopoulos, which in Greek sounds like a grammatical monstrosity.
Other surnames were commonly mangled in weird ways - Nicholas Metropolis (of the Metropolis-Hastings algorithm) surname was Μητρόπουλος (Mitropoulos). Metropolis is quite near phonetically but grammatically makes no sense in Greek.
Yes, people (specifically women) with strong opinion on the suffix of their name exist and proper solution of government is to butt off that decision. This is no the norm worth keeping by force.
I would note that in Spanish-speaking countries, it’s generally the case that a woman does not take her husband’s surname, but simply keeps her own. She might add de + her husband’s name to her own after the marriage,¹ but this is less common than women in English-speaking countries retaining their name after marriage.
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1. When my ex-wife’s green card was processed after our marriage, the attorney had added “de Hosek” to her name which she didn’t want and had to have the attorney change everything to keep her name as it was.
Slovene, which has roughly the same gender and case as other Slavic languages manages to not have gendered surnames. So, e.g., Pirc Musar and her husband Aleš Musar have identical surnames. Czech, on the other hand, will cheerfully rename Hillary Clinton to Hillary Clintonová, applying their rules for gendered surnames to foreigners when writing in Czech.