Ok, I've looked at Commons. It seems that names are added automatically based on the English label of the name ; meaning that if Яковлев English label changed, all people bearing Яковлев would be categorized in a different category from Yakovlev (which have a really small chance of happening between English and Russian, but there are other languages for which different transliteration systems coexist). I would say the category is about the Latin-script string in this case, since it's the only one not at a risk to change.
But there are technical ways to deal with the choice Commons made to be exclusively in English. The most obvious would be to create a template at the top of every name category stating:
"This category concerns people named 'Yakovlev' and 'Яковлев'"
We should also add related names too, like "Jakovlev", in another section. And probably add explicitly the writing systems ("'Yakovlev' (Latin script) and 'Яковлев' (Cyrillic)"), because for other examples it's not so clear:
"This category concerns people names 'Han' (Latin script), '韩' (Simplified Chinese), '韓' (Traditional Chinese), '한' (Hangul), '伴' (Kanji), and '坂' (Kanji)"
By the way 伴 in Japanese can be pronounced Tomo, Tomono, Tomori, Ban and Han.
It would be a system similar to the one existing on the French Wikisource, were we do use Wikidata to classify authors, and where we want Чехов to be with the T (Tchekhov), but eventual American Chekhov to be with C.
Wikidata should be able to deal with language-to-language combinations.