Why is Beethoven's "Moonlight" Sonata called that?

The Writer's Almanac for March 3, 2014 with Garrison Keillor:


Beethoven's "Moonlight" Sonata was published on this date in 1802. Its real name is the slightly less evocative "Piano Sonata No. 14 in C Sharp Minor, Opus 27, No. 2," and its Italian subtitle is translated as "almost a fantasy." In 1832, five years after Beethoven's death, a German critic compared the sonata to the effect of moonlight shining on Lake Lucerne, and the interpretation became so popular that, by the end of the century, the piece was universally known as the "Moonlight Sonata." Beethoven himself had attributed the emotion of the piece to sitting at the bedside of a friend who had suffered an untimely death.