Probably not the most official name, but I have heard them called "eyebrows." Is this the type of thing you mean?
Thats exactly what I'm looking for. I really want to do something like that over my garage doors. I've searched for about 2 hrs looking for pics or a website that might have pre drawn plans for one.
Well I don't know the exact issue but Better homes & garden had plans for a type of trellis/pergola that framed the garage door. It was really very nice. you can try looking for it on BHG.com
Here are some more photos of one. I stumbled onto this blog about a year ago. The homeowners are documenting all the remodeling to their craftsman bungalow. http://hillsdalehouse.blogspot.com/2007/09/weekend-project-trellis-over-garage.html
You might check you local library for this book or something like it: http://www.amazon.com/Quick-Guide-Step---Step-Construction/dp/1880029871/ref=sr_1_3?s=books&ie=UTF8&qid=1325132840&sr=1-3
I have found these Creative Homeowner series of books quite helpful in the past. This may or may not have the plans you need.
Simply sketch something out you like and a good carpenter can create them for you. Try to use plastic type woods such as Aztex as the material will not decay or rot. Any wood that has flat tops such as you will find in a trellis will hold water and decay from the top down. But with these plastic man made to look like wood products you get the best of both worlds.
Pigeons roof is the term I've used.