In the Kelvin timeline, the SS Smallwood was a civilian Federation starship, an Oberth-class science vessel in service in the 2260s decade.
History[]
The USS Enterprise received a distress call from the Smallwood in the Menzies 216 system, supposedly a place where no Federation ship had been before. The Smallwood was under attack from a pair of Klingon birds-of-prey near Menzies 216 V. The Enterprise intercepted the Klingons to rescue the Smallwood when another bird-of-prey uncloaked. Moments before the Enterprise was overwhelmed and destroyed, its communication officer Lieutenant Nyota Uhura realized that the Smallwood's translates to Kobayashi in the Japanese language.
The entire assault turned out to be an illusion by the omnipotent Q and was deliberately based on Starfleet's Kobayashi Maru scenario. (TOS - The Q Gambit comic: "Part 1")