No, the intended system has worked fine before the bug.
And the naming system works with the intended system. Boys get a name from their father's culture and Girls a name from ther mother's culture.
And some AI-Clans start with no young heroes who are married, if they marry a hero from another culture, the clan will get the wrong governor penalty and if the faction enact "Debasement of the Currency" the clan gets an rebellion, because the AI can not handle a -2 Loyalty penalty.
About your second point, I think this is an oversight that should be fixed/changed (e.g. clans only appoint governors of their culture/right culture).
But my main argument as to why I don't like the intended system (nor the bugged one) still stands. Currently cross-culture marriages happen frequently. In the intended system as well as the bugged one, children from cross-culture marriages are much more likely to inherit the culture from their "foreign" parent . When these children become clan leader, the culture of the clan would change - resulting in a -3 wrong owner culture penalty in the original fiefs of the clan, most likely leading to rebellion. Kingdom would then lose fiefs of their culture just because one clan's culture flipped thanks to an suboptimal marriage.
In most AI marriages the wife joins the clan of her husband and thus also the kingdom of her husband.
Assuming that the husband has the culture of his kingdom, children inherit culture like this:
Current bugged system: children always get culture from their mother --> child's culture always different from kingdom culture.
Intended system: Boys get culture from father, girls from mother --> daughters will have different culture than kingdom.
My suggested system: Since child is part of the father's original clan, they always get culture from father --> child's culture always same as kingdom.
In the rare scenario that the husband joins the clan of his wife and her kingdom (afaik only when female clan-leader marries male non-clan leader)
and assuming that the wife has the culture of her kingdom:
Current bugged system: children always get culture from their mother --> child's culture always same as kingdom
Intended system: Boys get culture from father, girls from mother --> sons will have different culture than kingdom.
My suggested system: Since child is part of the mother's original clan, they always get culture from mother--> child's culture always same as kingdom.
To conclude, in my suggested system the culture of a clan would remain fixed. Thus, the wrong owner culture penalty would only occur in conquered settlements or when an foreign clan is granted a native fief. It also prevents half of an Kingom's clan of changing culture after one generation. In my opinon it also more sensible that a clans culture would remain consistent and not flip flop through the generations.
Of course, this means that you could not change the culture of an clan. I think this would be fine for AI clans, but not for the player's clan - which is why I would also suggest that the player can decide which culture children of his clan will have (by deciding in which language a child is educated in), so that it is possible for the player to switch culture. If necessary, you could also implement a smiliar feature to change an AI clan's culture (e.g. convince/force an vassal clain to educate their children in the kingdom's culture).
PS: Sorry for the lengthy post.