See Varangian for the meaning of the name.
During the Russo-Japanese war of 1904-1905, Varyag accepted a badly uneven battle with a Japanese squadron in the Tsushima Straits on February 9th, 1904. When outmanned and outgunned, the crew decided not to surrender, but to sink the ship and die.
The famous Russian song "Krejser Varyag" glorifes the event.
The event is not to be confused with Battle of Tsushima, a decisive battle of the war, May 1905.
The name was inherited by the hapless Soviet aircraft carrier Varyag (which is informally called Varyag Cruiser, e.g., in press) and some other types of Russian armament.