Haha.. I really appreciate the fact that you were curious about the moon’s photograph that is featured on a late night talk show.
Conan the talk show premiered on November 8, 2010. But it was a waxing crescent on November 8,2010 at 11:00 pm, Los Angeles CA.
And if one were to be really nitpicky about this,by 6:30pm on November 8, 2010 the moon would have already set and you most certainly would not see the moon on the night sky at 11pm.
Therefore, not really sure what the moon is trying to represent here.
Also the moon keeps changing its orientation over the course of one day. And if you decided to look at the moon each day at the same time , it would be look slightly different.
Moon over the course of 24 hours
But the moon on Conan’s show is mostly Static.
Unless he decides to replace the already ridiculously big moon (Diameter: 3,475 km) that only is supposed to occupy ~0.00106% of the celestial hemisphere in the night sky by a Death Star (Diameter: 100 km to 160km ) of the same size!
So.. I guess that answers your question.. Have a good one!