Open a drawing, right click the drawing sheet and select edit sheet format. Move your mouse over to the text where the part name was displayed, right click it and high light all the text it in, go over to your text dialoge box [where the feature tree usually is] and select the "link" button [has a little chain link in it], scroll down the list until you find "SW-File Name" and click it.. hit the check mark to drop the text in place and then right click the drawing sheet, select Edit Drawing and then save the drawing as a "drawing template". Also click File/Save Sheet Format and save the "Sheet format" you've created in the same place as your templates [or where you've pointed your version of SW to "look" for sheet formats].
Voila.. the next time you insert a part into a drawing it will show the part name. You can also use this to put in the part weight, the material or whatever else you want on that list.. also.. that list is customizable through the "properties" of the parts or assemblies and there is no limit to the number of things you can link.