According to this link, it’s possible to put a visible dot on the moon with a laser:
http://www.k3pgp.org/viseme.htm
Arjuna34
Don’t you mean the SeaRiver Mediterranean? 
All right, so it looks like the OP’s idea won’t work, but how about the opposite effect, similar to what is suggested by the comic strip Mostly Clueless linked to or that Chairface Chippendale attempted: writing a message by darkening instead of illuminating the surface of the moon? But where they both carved into the surface, which I don’t think would work very well, I’m proposing just blackening it.
Let’s set aside for the moment any wussy complaints about permanently defacing a pristine natural landmark. (And if you really want to know, I’ve never bought into that virginal moon bit anyway. She’s been around, if you know what I mean.)
Anyway, shouldn’t my plan be much easier, for many reasons, not the least of which is that theoretically you could take as long as necessary? So what mechanism could we use to darken the lunar surface? Could powerful lasers burn the lunar soil? How much energy (and time) would be needed to have visible effects? Could a ground- or LEO-based laser create a fine enough point to draw a line on the moon’s face that would be resolvable by the naked eye? Or do laser beams spread out too far over 240,000 miles?
If so, what if we put a robot ship in selenosynchronous orbit around the moon? That way, we wouldn’t need as much power, although the power source would have to be portable.
Or, doing away with the laser idea, could we drop some sort of physical material onto the surface to write our message, like a giant ink-jet printer?
Or do you have a better idea?
I’ll assume:
[ul][li]Use black dust/powder, particle size 1 micron[/li][li]The “black” part doesn’t need to be completely covered by dust; a 10% coverage would probably produce a visibly darker shade of gray. [/li][li]The dark part would cover 5% of the moon’s disk[/li][li]Dust particles have a density of 1 g/cm[sup]3[/sup][/li][/ul]
This would require 50,000 tons of dust. About 3000 Saturn-V flights should do it.
The ironic thing is that Squink got more of less your answer after muffing the calculation (a 3.5m telescope has 250,000 times the area of a 7 mm pupil, not 25 million times).
-Note to self; mm are not cm. 
That takes the laser down to only 4.8 megawatts, which certainly seems more reasonable.
Thanks for checking Steve.
No comment on the OL, I just love pointing this out and do it every chance I get - a selenosynchronous orbit has a period of approx. 28 days and is 238,000 miles out.
What object is already 238,000 miles from the moon?
It seems extremely unlikely that’s possible with today’s technology. You need a visible light continuous laser, not a pulsed laser or an infrared laser.
It’s true there are military chemical lasers in the megawatt range such as the Boeing YAL-1: Boeing YAL-1 - Wikipedia However these are infrared lasers not visible to the eye, which is useless for advertising.
This web site says the most powerful known visible light continuous laser is 500 watts: General Laser FAQ - www.LaserFX.com
To simplify things, assume the laser is positioned ON THE MOON aimed at earth, and has a 1 milliradian beam divergence. The dimmest point source visible to the naked eye is a 6th magnitude star, under ideal conditions. That star produces a light flux of 2.5E-10 watts per square meter.
A 500 watt, 1 milliradian lunar laser aimed at earth would make a spot about 238 mi in diameter, for an area of 44,465 sq. mi or 1.159E11 square meters. The luminous flux would be 500/1.159E11 or 4.3E-9 watts per square meter, 17 times brighter than a 6th magnitude star, but that’s still only a 3rd magnitude star, still pretty dim.
That also assumes zero atmospheric attenuation and the laser’s spectral efficiency is equal to the white light from a star (which is unlikely).
If you can just barely see the most powerful visible light continuous laser if it were mounted on the moon aimed at earth (looking directly into the laser), there’s no way you could see the reflected light of the laser if located on earth and bouncing off the moon, esp if the energy was dispersed over a broad area to draw a logo.
However in 1993, a Georgia-based company, Space Marketing Inc., announced plans to launch square mile size billboards made from mylar sheets into low orbit. Logos about the size of the moon would have been visible to millions of people on earth. Strong public opposition caused them to withdraw their plan.
I think you misunderstand the problem. Beaming light to the moon efficiently is very easy. Given a laser, an amateur-size telescope is all you need to focus it on the moon. You don’t gain anything by moving the light source close to the moon.
The problem is this: because the moon is so far away, you have to illuminate a large area on the moon to make it visible from the earth. If you want to draw a pattern, the line width must be hundreds of miles. It doesn’t matter if the light source is on earth, or on lampposts installed on the moon surface; it still takes the same enormous amount of energy to create this continent-sized illuminated pattern.
You wouldn’t haul the stuff up from Earth. You’d mine it/make it on the moon. There are areas of lighter and darker material. So you go and dig the stuff up, then you pack it in ballistic cylinders that are designed to explode at a certain altitude above the surface and spread the material in a specific pattern, like a circle. Then you draw your characters with a dot matrix of explosive charges fired from a portable mass driver located right at the mining site. Without an atmosphere, it should be possible to do pinpoint ballistic trajectories to land the stuff wherever you want.
So basically, you arrive at a nice field of very dark material. You dig it up, stuff it into cannisters, load them in your mass driver, which is really a giant-scale print head. It modulates the power and angle of the muzzle to fire the cylinders where they need to go. Voila. Instant printing press - lunar scale.