This is very obviously about the episode nine montage and, well, everything that happened in that episode, but the whole thing goes way back to Mei's introduction, if not further.
Mei is Nonoka's fan first and foremost, and Kano tries to correct her, but ultimately fails as the series goes on. We already knew that Kano doesn't feel particularly good about her old self, but after the events of this episode it becomes much clearer what the name "Nonoka" means to her.
Yukine stopped having a daughter. Or more accurately, she stopped having her daughter and replaced her with an idol persona, only acting motherly to keep her dreams afloat (on an unrelated note, I think she treats Mero the same way, considering how Mero thinks of her). Kano expresses discomfort in her persona, and even more so, when talking to her father, she feels happy to be called by her real name for the first time "in ages". She discovers the mural and falls in love with its weirdness, with its expressiveness, and writes lyrics about how it gives her the hope she can shine on as herself.
Kano knows better than anyone how much names affect your perception of someone, she experienced it first hand. Which leads us to Yoru/Mahiru. Kano has been using "Yoru", Mahiru's artist name, all the way until episode 7. That is when she starts seeing Mahiru as much more than an artist. It's interesting, knowing Kano prefers going by her real name, and specifically asks her if she also has a preference. It is one of the many ways she parallels yet differs from her mother, from chasing numbers to registering creator and person who creates as different terms (Yoru and Mahiru, Nonoka and Kano).
In the fallout, the lovely line of "you're just a jellyfish who can't swim" starts with Kano correcting herself from using "Mahiru" to using "Yoru", because at that moment she was betrayed by the artist who went behind her back and teamed up with the enemy, and yet when she's by herself she still says Mahiru, because she was betrayed by the friend who values working under her mother more than her.
Mahiru stance to "Yoru" is pretty unclear to me. At the start of the show it is a name she has abandoned, alongside her artistic expression, for fear of being made fun of. But when she gets asked what she prefers, she says Yoru is fine. I think for her, now that she's grown back into her passion, they mean the same thing. Which also alludes to her choice. She wants to draw and to improve and to do anything to become better. Mahiru is slowly becoming more Yoru, and that is exactly what affected her relationship with Kano.
And that is without even going into Mei not being fully Japanese and therefore bullied as child for being called Kim, until she changed herself to fit in. Or Kiui finding confidence in her name and her uniqueness until it was stripped away from her once she didn't grow out of it, becoming a shut-in and expressing herself under the alias of Nox.
In conclusion, knowing how much I struggle to name my own characters I feel bad for the writers who had to come up with so many but goddamn if that doesn't elevate the story so much more. This episode was pain and I really wish hopeless lesbian Kano learns how to communicate about what her past means to her, since she's been failing at that from the very start of the series.