As everyone said already, the gendering isn't something just cultural, it's baked into the grammar. Specially because of grammatical case, different genders have different inflections. In a setting like "Let's call Kuznetsov(a)" accusative case applies, so Kuznezov would become Kuznetsova, Kuznetsova would become Kuznetsovu. Gender-neutral speech is absolutely impossible without overhauling the whole grammar, not just pronouns like in English. And yes, to a unaccustomed Russian ear applying third-person plural "they" to as indefinite-gendered singular sounds weird - and singular neutral "it" is just degrading, as I think it is in English.
Although in at least some cases the gendering isn’t just a simple gender marker: In Czech, for last names which are adjectives, then yes it’s a gender inflection (e.g., Rosický → Rosicka), but for non-adjectival names, the female version is expressed as a possessive, so, e.g., Hošek → Hošková, which to my liberal American ear feels kind of weird.
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.
