Actually it does have a model name, very conspicuously on the top tube. I can make out the first two letters.

If you could post a picture of the whole bike, or just read the top tube, we could identify it. But based on what I'm seeing, it is not worth spending hundreds of dollars putting STI on this bike. The furthest i would go is to swap the down-tube shifters for bar-end shifters. Still a worthwhile improvement, IMO.