I just need the round cover that has the Suzuki sign on it. What is that called and where can I find one?

That's the right side ignition (case) cover.  I believe KevinC has a couple for sale.  If you do a search in the For Sale section you'll likely find some.

Do you need the whole thing or just the little plate that has "SUZUKI" stamped on it?

I have one that was machined out of billet aluminum. $50+ shipping. Its silver and does not have the suzuki logo... and doesn't need foil cover. And it is solidly made... quite possibly the strongest part on the motor.
Cool.
Srinath.

The engine case cover and the foil cover with the Suzuki logos are available separately.  The foil disc runs about $10-15 from a dealer or BikeBandit.com or RonAyers.com.  The stock case cover is rather pricey; enough that $50 for Sheshadri's heavy-duty version is an attractive alternative, if you don't plan to also invest in case savers.

I had the same problem, I took the cover off and repainted it with Krylon Gloss Black and it matches the factory paint exactly. Then I got the logo from bikebandit.com and it looks just as good as new, the logo was about $13.

If you're really nitpicky, you can use bondo to fix the gouges and re-paint it.
It's not worth buying a new one unless it's completely mangled and you have no choice.