In 2375, the Musashi was involved in a series of complicated trades for engineering equipment orchestrated by Ensign Nog of Deep Space 9. Nog traded an induction modulator to the Musashi in exchange for a phaser emitter. (DS9: "Treachery, Faith and the Great River")
According to the Star Trek Encyclopedia (4th ed., vol. 2, p. 59), the Musashi was "named for the Japanese dreadnought that sunk in the Sibuyan Sea on October 25, 1944 during the Battle of Leyte Gulf."