Make sure food doesn't stay in the very bottom part for long enough to burn on. The flared sides and narrow bottom of these pans tend to concentrate heat at the bottom, and burn on food more easily than flat-bottom saucepans and frying pans. Once food is burned on, there is no way to scrub it off without also removing the nonstick coating. It only takes one batch of fried rice or browned onions to permanently wreck the pan. Finally, stir-frying involves a lot of vigorous motion with utensils, which rapidly wears out nonstick layers. With nonstick woks, it is simply a matter of time before they are ruined.
My suggestion is to replace your teflon wok and kadhai with (respectively) carbon steel and cast-iron equivalents at the earliest convenience. Woks and kadhais are designed for high-flame cooking, and if you reduce the heat to protect cookware, then the food won't get browned fully. With these materials you can use full heat without ruining pans or releasing toxic chemicals (from overheated Teflon). Cleanup is simple: just rinse out, scrape off burnt bits, wipe them down with a paper towel, and season with oil.
Finally, wooden or silicone rubber utensils are the best for a nonstick wok or kadhai; they won't scrape off the nonstick layer unless used very roughly, andthey can stand the heat without melting. Normal plastics (particularly polyethylene or polypropylene) tend to melt, and metal will scrape up the nonstick coating.
If you're particularly anal about the looks of the inside of your grill there may not be a solution, otherwise clean the inside as best you can and coat with an oil based cooking spray. Season the inside after spraying by bringing it up to cooking temp (about 350 degrees) without food for about an hour and let it cool. If you over heat the grill sometime during the summer or you live in a particularly corrosion prone environment you may have to repeat this at the end of the season for winter storage without rust.
Best Answer
I don't think there are any 'official' names, but I suggest: