Charlie is of course a casual nickname for Charles, a more formal, royal name that means "Free man." While Charles is the 62nd most popular name in the U.S., Charlie is quickly creeping up, and nearing the top 200. While most of the most famous "Charlies" started life as Charles, Charlie Chaplin, Charlie Brown and Charlie Sheen are all famous namesakes.
West is the most popular of the "directional" baby names (though something tells me when we get the official Social Security list next week, North may have made a very strong showing). West was actually a top 1000 name first back in the late 1800s and early 1900s, and hasn't been seen in the top 1000 since—though I think it makes a stronger showing as a middle name instead.
All in all, Charlie West Arquette is a pretty cool name. What do you think?