It's known as a pergola or arbor for supporting planting and/or providing shade (a trellis is a vertical planting support).
There are many sources for pre-fabricated kits. Try googling "window pergola, window arbor, garage pergola and garage arbor kits."
However, such a structure is not difficult to design and build.
I would avoid adding planting because it so often destroys eaves and gutters of a house. Carefully flash and seal any penetrations through the wall cladding.
When I renovate a house planting structures, it they are still intact, are torn off along with a lot of damaged wood. IMO planting should be at least a foot from a house. 2 feet is better unless you are willing to prune frequently.
Here is a link that might be useful: arbor kits