This sounds like a question for Munroe’s What If. My completely uninformed guess is that it would take many rockets to make a sufficiently-large splash.
I agree. The surface of the moon is 4E7KM^2. Assuming you paint only one side it's slightly bigger than the surface of Russia.
It's silly to paint near the border of the visible side because the surface is almost tangent to the line of sight. It's better to paint the central part and keep the border white. (It's also better if you want contrast with the background or your logo has a withe circle around it.)
Anyway, painting only the central half of the visible surface, it's 1E7Km^2 that's slightly larger than the surface of Canada=China=USA.
You would not need to paint the entire visible surface, you could settle for filling in a crater like Tycho (which is smaller than the state of Delaware). That would still get folks super mad!
