I guess the artist didn't want to draw Yuuki obscured by shadows or panel angles for the entire conversation? I'd already spoiled myself so I read the LN knowing that the "boy" had to be Yuuki, but other than some strong hinting they never explicitly mentioned who he was so this chapter came as a surprise to me in that they just straight up said it.
Can't withhold visual information in a visual medium without really going out of your way to do it.
It'd be great if they just revealed him without having his name up in a dramatically gigantic speech bubble, though. Some readers might've missed who he was (lol) that way, just like how some people don't clue in on who he is in the LN because they're thinking about other things while trying to get through the chapter or something.