I did this, but for some reason it didn't work. Are you sure it isn't an Illustrator issue? In all other programs the file name shows when I minimize them.
Can you post the snap shot of the taskbar if possible so that I can understand your problem correctly?
Sorry I didn't get back to you. I was at home all weekend and the problem is with my work computer. I have a Mac at home
Anyway, I talked to someone in the IT dept and while he was fishing around, I got the idea of setting my appearance to "classic" instead of one of the newer appearances. It seems to have solved the problem. The appearance may be boring, but at least I got the result I want.