By the end of the series, this is still unclear, perhaps deliberately, but the evidence points a bit towards Nao having realized.
After episode 10, Ink can no longer transform into Pastel Ink, but she decides to cosplay (poorly) as Pastel Ink anyway in episodes 11 and 12 and help Nao with his studies. Mio, who had not seen Pastel Ink before this, immediately recognized her as Ink. However, when Nao sees Ink wearing this outfit, he first calls her "Ink" but then immediately changes it to "Pastel Ink-sensei", the same way he called her before. Mio is annoyed by her brother's apparent cluelessness at this. However, given the context of the scene, it's also quite possible that this change was out of consideration for Ink.
Furthermore, at the end of episode 12 (the last episode to have this Nao and Ink), Nao also says ambiguous lines to Ink, to the effect of "I haven't seen Pastel Ink since then, but I'm sure if I ever needed her help she would show up again." Given that he was talking to Ink, this could be an acknowledgement that he knows Ink was Pastel Ink in a way that remains ambiguous. He could still just be clueless, but the way this statement is phrased, it seems like he's thanking her in a way that doesn't give away the fact that he knows she is Pastel Ink. Nao's actions in all of these scenes are of a slightly different character than his interactions with Ink and Pastel Ink in the first 10 episodes.
Exactly when he realized is difficult to determine. There is one scene earlier in the series in which he sees Pastel Ink and has a vision of Ink. There are also several scenes between the two in which he seems like he's going to say something important, but backs out at the last moment and says something relatively trivial. At any of these points, it's possible that Nao is actually aware that the two are the same, but it's also possibly just a running gag that he is clueless.
With that said, there's nothing in the series which explicitly refutes the idea that Nao is just incredibly clueless and never realized even after episodes 11 and 12. But at the very least, it seems like a reasonable interpretation that by episodes 11 and 12, Nao is aware that Pastel Ink is Ink, and that he's only playing along to avoid upsetting her. There unfortunately just doesn't seem to be any more definitive statement that can be made based on canon sources here.
