Just a quick note about the translations in this chapter:
Nanami does in fact slip up and say "Kaoru" at the end, as you can see here:
Necrobump for some added context for others: The whole thing with Kaoru/Kaori's name is it's literally the same kanji 薫 for both.
That's why Ryuji commented how strange it was for Kaori to have that name when her brother's name was Kaoru... and then Nanami thinking to herself "Of course... no family would ever do that..." -- because it would be impossible to tell their names apart when written down unless you had context. Going through the raws, Kaori is always written in the dialogue as かおり instead of the kanji 薫 (probably so the readers also know which name is being said specifically) and in this one instance the kanji name is used rather than the hiragana.
So presumably the implication is she accidentally said Kaoru instead of Kaori, and her mom didn't react to the slipup. (Although IMHO it's been implied since early on that her mom heavily suspects Kaori is a boy, but can tell they're a good person and a good friend to Nanami, so they've said nothing about it to protect him from the father heh)