>>3370793>>3370811Shinji almost certainly knew Rei before the show begins.
The first time the name "Ayanami" is spoken is when Shinji's in the bath in episode 2. But everyone else- Gendou, Misato, Ritsuko- has hitherto only called her Rei. So he must have prior knowledge of her.
Cf. in episode 20 when Shinji seems to have a young Rei in his memory, and he accuses Gendou of abandoning him since he had Rei.
Shinji regularly met Gendou until three years prior to the show began, presumably he would have had some meeting with Rei on some of these occasions also.
Note also that Shinji has, apparently, seen the members of the Human Instrumentality Committee- probably in some sort of hearing shortly after Yui's evangelization (we see this in episode 12, right before the operation against Sahaquiel begins).