I think they’re…right-minded, but really corny and tone-deaf. The main point is that Tsuna has a meaningful name, has a very Japanese Don’t Rock The Boat attitude, and the fact Kou outright changing her name wouldn’t go unnoticed, I figured the best bet was simply to read her kanji differently – it’s not uncommon to correct people with “actually, it’s read ___”, and some people even ask you how your name is pronounced before trying, so Kou can slide her name right in there. It’s just incredibly silly she tried it with a kanji as unambiguous as 綱 . I’m sure she can get away with saying it’s a kirakira name based on the shogunate. She’s almost not wrong
So that’s a characterization thing. If you want like, actual names Iemitsu would give his cis daughter:
– Chiyohime (Tokugawa Iemitsu’s daughter)
– Tsuruhime (Tokugawa Tsunayoshi’s daughter, also the name of Tokugawa Iemitsu’s adopted daughter)
– Tsuhime (Tokugawa Iemitsu’s adopted daughter)
And so on and so forth.
I think ‘Tsuhime’ is the funniest because Gokudera would call her ‘Tsuhime-hima-sama’