I didn't realize until today that the full name of the Donetsk International Airport in the eastern part of Ukraine is actually the Donetsk Sergey Prokofiev International Airport. It may be the only airport in the world named after a composer. The Wikipedia states that the airport "was built in the 1940s and 1950s and rebuilt in 1973 and again from 2011 to 2012. The airport is named for 20th-century composer Sergei Prokofiev, who was a native of Donetsk Oblast." Unfortunately, Ukrainian forces and separatist Russian forces have been battling over the control of the Donetsk Sergey Prokofiev International Airport. This Reuters report shows recent photos of the destruction. Hopefully, someday soon the airport will be reopened, and all people (including musicians and composers) can safely fly in and out.
After writing this, I remembered that Poland has the Warsaw Frederic Chopin Airport. So there is at least one other airport named after a composer.