I would suggest to manually download the drivers from the AMD site. But for that yes, you need to know what exact model you are using!.... At times, due to loose or faulty connections in the PCI slot, the Auto-Detect software might just not work.
Do you want to install the AMD driver best suited for your GPU? If yes, and AMD auto-detect cannot identify your hardware. Then there might some problem with your GPU. Can you take it out and plug back into the PCI slot? See if it works?