That is all well and good, but it does not explain why her family themselves kept the name and the lore for so long.
I think there's an example of this in American cutlure -- slavery.
My ancestors owned slaves. One of those ancestors fought for the Confederacy. I could tell you the name of one of the descendents of the slaves my ancestors owned, and a good many posters here would recognize the name. (There's even a tangential
Star Trek connection; no, it's none of the actors. I won't share it, so don't ask.)
I personally am disgusted with this knowledge. I judge my ancestors harshly for what they did.
Not all Americans with slave-owner ancestors feel this way. Southern pride is a thing. My late aunt, who was
not descended from that branch of my ancestry and whose only Civil War ancestors fought for the Union, used to post neo-Confederate propaganda on Facebook in bygone days. I live in Pennsylvania, a northern state, yet I see various Confederate flags here frequently. (The house across from where I used to vote has flown a Confederate flag for years. A back road here is the only place I've ever seen the Blood-Stained Banner in the wild. A nearby house flies a flag that mashes the US flag with the CS battle flag.)
But that cultural pride on an individual level has also become a political movement. Look at the nonsense surrounding "woke" and "Critical Race Theory" on the right. Look at the promises by Republican candidates to restore the names of Confederate traitors to recently renamed Army bases. Look at Florida's new education standards that tries to paint a rosy picture of slavery, that it taught slaves valuable life skills.
This isn't new. You go back in time ninety years, to before World War II, and you have things like the German-American Bund, an organization that didn't just promote German pride; they held
summer camps for children to indoctrinate them in Nazi ideology and staged
a Nazi rally at Madison Square Garden, melding pride in German heritage with American patriotism and creating an American fascist movement.
The point is, some people will take pride in their ancestry, no matter how repugnant it was and is, because it lets them connect who they are to where they came from. And others look back at where they came from and repudiate it.
La'an is clearly one of the latter. The past happened, she can't change it, it disgusts her, and she carries the knowledge and the guilt with her. I totally get that. I also get why she can't or won't change her name to bury the past, because her name is part of her identity. She can't run from her name any more than Robert E. Lee's descendents can run from his. Maybe she thinks she might even redeem it.
So La'an carrying her full name doesn't bother me. La'an's parents and their ancestors carrying it doesn't bother me. It's just the reality of living with the knowledge that your ancestors did monstrous things.
What does bother me is Kirk and Spock not saying right away, when they meet Khan in "Space Seed," "'Noonien Singh'? Why, that's funny, I know someone with the same surnames, what are the odds...?"