The SS Tsiolkovsky (NCC-53911), also known as К. Э. Циолковский, (Romanized from Cyrillic: K. E. Tsiolkovsky) was a 24th century Federation Oberth-class starship operated by Starfleet. The Tsiolkovsky was built at the Baikonur Cosmodrome, USSR and commissioned on stardate 40291.7.
Eight months prior to stardate 41209, in 2363, the Tsiolkovsky was assigned to observe the collapse of a red supergiant star. During that mission the crew fell victim to a form of polywater intoxication. After losing contact, Starfleet ordered the USS Enterprise-D to investigate the fate of the vessel and its 80 crew members.
The Tsiolkovsky was discovered adrift in space, its bridge open to space due to an open emergency hatch, with all hands lost. When the Enterprise-D crew became infected with the same virus, and was in danger from a stellar core fragment, they bounced a repulsor beam off the Tsiolkovsky, which pushed the Enterprise-D away from the fragment, providing the necessary time needed to restore power to the engines and warp away. While the Enterprise-D survived, the Tsiolkovsky was destroyed. (TNG: "The Naked Now")
|USS Biko • USS Bonestell • USS Cochrane • USS Copernicus • USS Grissom • USS Oberth • USS Pegasus • SS Tsiolkovsky • SS Vico • USS Yosemite • Unnamed|
The Tsiolkovsky was "named for Earth scientist Konstantin E. Tsiolkovsky, whose work formed much of the theoretical basis for his world's early exploration of space." (Star Trek Encyclopedia (4th ed., vol. 2, p. 424)) In previous editions of the Star Trek Encyclopedia (3rd ed., p. 527), Tsiolkovsky was identified as a Russian space pioneer.
While the ship was called the S.S. Tsiolkovsky or the Tsiolkovsky in the script  and in dialogue, the dedication plaque listed the name of the ship in Cyrillic as К. Э. Циолковский, or K. E. Tsiolkovskii transliterated with current standards for passports, albeit with some characters misrendered – the plaque actually reads "К. З. ЦИОПКОВСКИЙ", or "K.Z. TSIOPKOVSKII" after Romanization.
A copy of the plaque was sent to the Tsiolkovsky State Museum of the History of Cosmonautics which is located in Tsiolkovsky's home town, Kaluga, Russia. (The Official Star Trek: The Next Generation Magazine issue 15, p. 34)
The Star Trek Encyclopedia listed this ship as the USS Tsiolkovsky. The SS prefix was used in the dialogue. The dedication plaque suggests that the name prefix was not part of the official name of the ship. While this is unusual, there are other examples such as the Raging Queen. The ship was listed as a Starfleet registered vessel with an NCC number in the plaque and there was a corpse wearing a Starfleet uniform on board.
The registry number on the studio model was originally not discernible on-screen in standard definition version of the episode. When the high definition copy of the footage was rendered for the remastered version of the episode, it was discovered that the model had the registry "NCC-640", carried over from its previous use as the USS Copernicus in Star Trek IV: The Voyage Home.
Michael Okuda remarked years later in this respect, "I seem to recall that Grissom may have been relabeled to serve as another ship (the Copernicus?) in Star Trek III or IV. I didn't try to relabel the model for 'The Naked Now,' partly because we realized that the existing registry would not be legible in standard-def video, but also because we were all so insanely busy at the time that no one could take on an additional project that wasn't likely to be seen on the screen." 
The number was digitally changed to its correct one from the dedication plaque in the first full side view establishing shot. Unfortunately, the digital artist overlooked the previous scenes and the later scene when the stellar core fragment smashes into the ship, as it there still carries the original, now discernible, registry number.