There's how his mom appears amused when finds out about it. If it were a random person there wouldn't get much of any reaction or entertainment from it. Much less any reason to follow along with the not telling him. Especially considering she outright says to him "Isn't it about time you guessed correctly?" should be indicative that he knows the answer whether he realizes it or not.
It should be clear by now that she wants him to figure out his name, right? Second chapter he acknowledges that it'd be impossible for him to know. Going off that, how many random people would really care whether or not you could guess their name or knew who they were. So there's two lines of thought, either a influential family lives there ("Do you know who my father/mother is?!") and it's someone he should know, or it's someone he knows/knew.
Then there's when she gave him hints that he took and ran in a whole other direction with. She told him her birthday and star sign, to which he assumed her name had something to do with crabs. The thought never occurred to him "Hey, I know someone with that birthday...". Nah, bro. Her name obviously has crab in it.
There's when Mahiru arrives and he finally decides to use his brain by pinpointing her year of education. When asking about Miya and Asaka he's told that they're all still friends and Miya even attends to same school as her. Then we come to these two chapters, the two know eachother, are friends, are roughly the same age, the same uniform. Sure, you can argue it's just as likely to be someone else (which I'd agree), but at this point he knows:
Her birthday, she happens to be friends with and attends the same school as Mahiru, by his mom's reaction to the name game it's someone he should know, the likelihood of a random person versus it being someone you potentially know making a guessing game about their name.
Honestly, there are arguments you can make against those reasonings, but the fact alone that the thought and/or possibility never crosses his mind because "There's no way I know someone that beautiful"... Just... Really bro, really? That's what we're hung up on here?
