It's very hard to erode it because Russian, as all Slavic languages, is very thoroughly gendered in general. It's not just nouns (including names) and pronouns, but adjectives and verbs also have gender that must agree with the noun they apply to.
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.