We expect a web site to give us suggestions as we start typing in the search box. This feedback helps us learn the lay of the land and see what else we might be interested in. It's certainly more convenient to see results as you type vs. having to hit "go" first and then see if anything comes up.
But there's another piece of useful info that could be included with product names in predictive search results: the location where the items live in the site's taxonomy.
In any digital world the information architecture is the map new users need to reckon with before they can fully understand what goes where and what they can do in this place. But beyond a simple list of things, they also want to know where those things are and also how they relate to each other.
So why not include another column in results that shows where things live in the ecosystem?