Yea, she might identify it as the 'Saito Groups' crest but not directly connecting it to Akane because it's not like Jun and Akane are bffs or childhood friends or anything remotely close and Akane wasn't really involved in the family business at all. She would come to know of it as she grew up but wasn't involved. 

[hider]
We once talked on the group chat on skype about a potential connection between them but it was never fleshed out or talked about more. There's a chance they could've met when they were little at a business meeting or such involving their fathers but that'd be it (that would make sense anyways) but even then, as stated above, her appearance and personality drastically changed so she'd seem like a totally different person and by in no way would be directly tied to 'Akane Saito' (especially since Jun doesn't know her that well to begin with). 

I'd say that maybe Jun picked up on her personality change and was reminded of a little girl she once met as a kid but they hardly came across each other at school. Maybe an off-screen thing considering they're both in the Kendo Club?
[/hider]