Yes, very good point. My initial thought was, didn't he go to school with all of them so literally now no one remembers him from kindergarten? I only thought that the spell was for people to forget Parker as Spider-man, not who Peter Parker is altogether (clearly it's the latter going by the aftermath).

My only guess is that, even though Dr Strange didn't go into specifics, maybe its assumed that his spell would also erase video and printed evidence of Parker as Spider-man, otherwise it would make no sense...or you've discovered a massive plot hole.