I think the ML didn't exactly knew it was her. He just heard her voice and Anrie's sounded familiar to him.
maybe it's gonna be explained in more detail later, perhaps that's it we'll see
From how I understood it, he doesn't know she is the voice at all.
Instead, to him, Anri represents change and something new. It's not quite love yet but it is budding. Anri is the representation that he CAN move forward with his life away from Elze and the Book. She's a new variable that had never existes before in his previous life.
Btw, idk if that's a plothole or not but like, if ML knows that MC is that disembodied voice that pitied him, why was he surprised that she knew his weakness and what not? Like, it just makes sense to assume if she knows of his "fate" she'd also know a lot about him.
Or was that moment where she yoinked his side like a confirmation of sorts? Maybe I'm too neurodivergent for this but if that's really it they need to make it a bit more obvious. Put a big circle and jiggle some keys over that shit idk.