There is no "canvas" in Illustrator. This is not a raster imaging program.
In Document Setup, Transparency pane, you can use the transparency grid as a fake "background" by setting both parts of the grid to the same color. Effectively, this makes the Illustrator window display as the color instead of white. But this is just an on-screen display, originally intended as a means to view transparency effects. It does not print. It is not the same thing you think of in terms of the "canvas color" in a raster program.
If you want your document to actually have a colored background, draw one. Get the Rectangle Tool and draw a large color-filled rectangle. Sent it to the back and lock it. Or put it on its own Layer and lock the Layer.
In Illustrator, you create and work with objects, not regions of different-colored pixels as in a raster program. If there is no object, there is no color, because there is nothing to which to apply the color.
Actually I think there i a way of selecting a slightly arker background that will not interfere with the artboard color.
Look in the preferance uner interface or something like that there may be a setting or perhaps in the document setup or the artboard tool settings.
I think you can.
What James suggest will chane the artboard color as well.
I was mistaken the color is a very light gray as it is and no way to change it.
There is a function to simulate printing on coloured paper (it is in the document setup window). Would that help you? This simulates on-screen what the art would look like if printed on coloured paper. Of course, this simulated colour does not print.
You simply cannot change the color of the pasteboard (the area around artboards) short of drawing rectangles and filling them with color.
Artboards can be colored in the Document set up dialog as others have posted.