The above picture is not my roof but nearly identical. Except my roof also has horizontal 2×4 supports. The previous owner has a shop light running horizontally screwed directly into the 2×4. I want to install a ceiling fan but am not sure how. I know I can install a box that directly mounts to the 2×4 that is fan rated but I thought the canopy of the fan would have a greater circumference than the box and there would be an exposed gap. Any suggestions? I would want a look like this 
Best Answer
You want the main attachment for the fan box to be attached perpendicular to the floor, not horizontally into a faming member. The twist on a horizontal attachment could lead to failure. The box should be attached with sizable screws or lag bolts.
That means, you should have a framing member directly above the box, either the 2x4 you mentioned or a short added framing piece running perpendicular (vertically) to the joist.
I would build a small wooden frame around the fan box. 2x or 1x pieces should do. They are not structural but decorative and gap filling. These will give a base larger than the canopy.
I would then run a conduit to carry the cable to the fan box, making holes in the surrounding box trim.