How can I ask a girl out when I don't even know her name? Should I?

All right so here’s the thing. I see this girl in college about everyday. She’s in the same course/programme as me. Just in a different class. I see her a few times a week when classes are being switched or when passing through the corridors… She’s really pretty. And I’ve noticed that she does look at me a few times but the minute I look at her, she turns her eyes away. I’m one of the more popular guys in my batch and I’m very sure she’s noticed me. The problem is, I don’t really know her name. Although I think she knows mine… I’d really love to go out with her and have really been thinking about her all the time. And I mean ALL the time. Even when I’m back home, in class, doing whatever… What should be my next step? Awww… She’s soooo cute… :-)

Btw, I’m 20 and haven’t had a girlfriend before. I liked a girl in high school a lot and asked her out but she already had a boyfriend. I’ve been searching for the ONE ever since… And now in college, I think I could really love this girl and care for her. How do I approach her? I dont even know her name! Is this a crush/infatuation/love? Btw, I’m pretty shy… :-(