In the opinion of Industrial Light & Magic art director Alex Jaeger, the starship Kobayashi Maru had a similar design to the USS Excelsior (β) that was planned to feature in the filmStar Trek but did not make the transition to the screen (although it was essentially a dark-colored variant of the Armstrong-type). Jaeger specifically commented about the Kobayashi Maru, "It resembled the Excelsior, but was more of a cargo version." (Cinefex, No. 118, p. 60; Star Trek - The Art of the Film, p. 59)
According to the virtual collectible card battle gameStar Trek: Rivals, card #41, the USS Kobayashi Maru has the registration NCC-S3700. The CGI model of this ship made an appearance in the Star Trek Encyclopedia (4th ed., Volume One A-L, p. 434) where the registry and name could barely be made out. The registry appears in the entry for this ship on the same page and in the starship list on p. 331.