Projection is too expensive
Advertising on the moon using projection would be so costly that it is unlikely anyone would pay for the advertising space. However, there are other methods of advertising on the moon. The convenient fact that the moon is tidally locked means that if you put a physical advert (rather than a projected one) on the moon's surface it would stay visible (at least during phases of the moon when the advert is lit by the sun).
A physical advert
Setting this up would still be hugely expensive, but if the advert could be changed simply by sending a signal from Earth, then running costs could be minimal. If an organisation were to provide the initial huge investment, over time it could be paid off provided that the design of the system required minimal maintenance.
For example, a vast army of simple robots that can display black or white could be spread out across the facing surface of the moon. They require no power apart from when a signal arrives to tell them to change colour for the next advertisement. That minimal power requirement can be covered by solar cells and a small battery. Ideally the robots would be mobile so that they can move around to cover any dead robots, so that a small number of failures does not significantly diminish the image quality. This would also mean they could be sent in large batches and spread out autonomously rather than needing to be placed.
The moon is black
Although the moon has a white appearance due to being only visible when brighter than the sky, it actually has a low albedo of about 0.12 (dark grey). This means that an area of the moon's surface covered with something white would appear from Earth as an area much brighter than the rest of the moon. Adverts on the moon would not just be pictures, but would be shining out brilliantly and difficult to miss.
Colour and animation
The same principle could be used with robots able to display red, green, blue or any combination. This would allow for full colour photographs to be displayed on the moon. Since the image would only be visible when that part of the moon's surface is in sunlight, the robots would have power and could change colour periodically provided they were provided with a timer which could be synchronised when the next advert is transmitted. This would allow for cycling through the colours required for an animation, so full colour high definition video could be played on the moon. The frame rate would depend on the efficiency of colour change and the power provided by the solar cells, but the resolution could be as high as the number of available robots would allow. High definition doesn't take more power, just more robots.
I've made this seem very easy (just expensive) but of course it is not quite so simple. The moon's surface is irregular and there may be parts that the robots cannot reach or regions too steep for them to settle on. The images may have gaps or lines where rough terrain or mountain ridges prevent colour being applied. Initial adverts may be coarse, low definition proofs of concept, with resolution being increased and gaps being filled gradually over time as investors are convinced by the influx of advertising revenue and start to invest more.
Of course covering the moon's surface would take a vast amount of material, but due to the relative brightness of white material (or red, green or blue material) against the dark grey of the moon's surface, leaving large gaps between the robots would just result in a less bright image. The colour would still be reasonably accurate as the moon's surface visible between the panels would contribute relatively little to the perceived image.
Part of the cost may be absorbed by combining the purpose of the robot army. There are plenty of scientific uses for a huge array of robots that can each point a sensor in a variable direction. A small robot with a large colour panel and a few small scientific instruments would appear exactly the same from Earth as if it was just a colour panel. Scientific funding may be provided to set up the robot array in return for control over what is measured, or sufficient investment may be gained based on the returns expected from selling both advertising space and time on the scientific array.