The name of this ship was derived from Ed Miarecki, the creator of the design study and filming model of the Buran.  As with the other kit-bashes for "The Best of Both Worlds", the USS Buran was a one-time use only model and slated to be discarded, but was saved from the dumpster by Visual Effects Coordinator Gary Hutzel, who took the model into his care. 
According to the Star Trek Encyclopedia (4th ed., vol. 1, p. 109), "the Buran was a "kit bashed" study model barely glimpsed among the wreckage of the "graveyard" scene in the episode. The ship was named for the Russian space shuttle, which was in turn named for the Russian word for "snowstorm"."