Most things in the solar system borrow their names from Greek and Roman mythology—think of the names of the planets besides Earth. Mercurian geography initially followed suit; the planet's albedo features—the patterns of light and dark visible through a telescope—were mapped and thus named by the French astronomer Eugène Michel Antoniadi in the 1920s. But in the 1970s, the double whammy of radio telescopy and a Mariner 10 flyby revealed a wealth of details needing names.
Craters on the moon had been primarily named for astronomers and scientists, for example, the prominent southern hemisphere crater Tycho, with its bright ray system, named for the Danish astronomer Tycho Brahe, or the crater Clavius, named for the German astronomer Christopher Clavius, and made famous as the site of the moon base in 2001. But for Mercury, on grounds of both avoiding repetition and general novelty, the International Astronomical Union decided to go in a different direction.
Mercury is a heavily cratered planet, with perhaps the greatest number of craters of any body in the solar system. After much discussion and no little controversy, the Mercury Task Group decided to name these craters for great human contributors to the arts and humanities, including writers, Composers, painters, sculptors, and architects. This system is consistent with previous decisions made for the Moon, Mars, and Venus, on all of which the craters have human names. In terms of commemoration of human achievement, Mercury will be the complement of the Moon, with the latter honoring scientists and scholars and the former honoring the creative and artistic heroes of mankind. Initially, all craters photographed by Mariner 10 and having diameters of 100km or more will be named, as well as selected prominent or geologically significant craters in the 40 to 100km size range.Still bringing up the rear, but better than nothing. The composers selected thus far (you can browse through this list) tend towards the standard European canon, although Charles Ives gets a crater of his own, as do the Indian composers Tansen and Tyāgarāja and the Chinese composer Chiang Ku'i (Jiang Kui) and his legendary countrywoman Ts'ai Wen-Chi (Cai Wenji). Beethoven gets an entire area (the Beethoven Quadrangle, which contains Schoenberg's crater, as seen above), as does J.S. Bach—the Bach region, near the planet's south pole, is dominated by large craters named for Johann Sebastian and Richard Wagner. (Mercury's planetary neighbor Venus, whose craters are named for notable women, actually probably has even more musicians on the list, from Francesca Caccini and Thekla Badarzewska to Kirstin Flagstad, Maria Callas, and Kathleen Ferrier to Patsy Cline and Josephine Baker.)
A number of scholars are assisting the Task Group in selecting these names. The distribution by fields will be approximately 50% for authors, 30% for artists, and 20% for composers. (David Morrison, "IAU Nomenclature for Topographic Features on Mercury," Icarus 28, 605-606 (1976))
The most contemporary composer representative on Mercury is Stravinsky. The IAU specifies that geographic features can't be named for anyone who hasn't been dead for at least three years, and the last round of Mercurian naming came in 1985, when a lot of possible honorees—Cage, Copland, Bernstein, Feldman, Xenakis, Tippett, not to mention a whole host of jazz and rock composers—were still alive. Their time may be coming, however: amazingly, only half the planet has ever been mapped (Mercury's revolutions about its axis correspond with its orbital revolutions around the sun, so the same face is always towards the Earth), but that is about to change, now that NASA's Messenger spacecraft has arrived at Mercury. The craft made its first flyby in January; another will follow in October, and then, in 2011, Messenger will go into orbit around the planet, allowing the first complete map of its surface. Make friends with an astronomer now, and your favorite composer might have his or her own permanent place in the sun.