I read her as pretty straight, so sadly I don't think that's an option, though considering her luck, I wish it was.
But, yeah, considering her luck with guys up to that point, it's really no wonder she accepted Tim being her squeeze while not knowing his name. It's like "Wow, this is fucked up, but he treats me like a HUMAN BEING, and actually cares about me, OMG, I didn't know guys could do that!" for her considering her experiences. I figure, character arc wise, that when she started wanting to know his name veryvery vehemently was when she got a better handle on her self worth and self esteem, which explains some of her questionable behavior.
Not to say that was Tim's fault, he's just a fourteen year old boy, how was he supposed to know all the screwed up issues his gf had? He was ecstatic that she'd be willing to date someone without a face, but never asked himself WHY, because he's just a kid.