[Aleise]

My own theory on the matter is that Shiori was looking for either Yuuichi or Ayu, since meeting the two of them was what made her stop cutting herself - but she's not really sure of which of them she wants to meet - leading to the unknown name (at this point she doesn't know either of their names), and confusion in the gender, year, and class of the person she's looking for.

I would think that the only lead she has of finding either of them was what Kaori told her - that the courtyard would be a popular spot (well, in spring, but Shiori can't wait that long). Since it was the spot that her sister told her, she couldn't help but think of her while she was there, leading to the staring at her sister's classroom bit.

Why do I think she's not looking for Kaori? Well, if she was looking for Kaori, why does she always leave the school after meeting Yuuichi? We already know she was willing to wait until late afternoon (that one time in . . . err, was it ep. 6?), so if she was really waiting for Kaori, she would have stayed there daily until late, regardless of what Yuuichi says . . .