The SS Buckaroo Banzai was a Terran BBI-993-type starship that was in service in the mid-22nd century. When this starship was launched in 2137 from Earth for a mission to Planet 10 (DIM-8), the Banzai was under the command of Captain John Whorfin.
This vessel was among the list of ships that appeared on Captain Jean-Luc Picard's desktop monitor while he searched for "all Earth deep-space launches from 2123 until 2190 with destination in or near the Ficus sector" during an investigation of an SOS signal discovered in that sector in 2365. This vessel, however, did not fall within the parameters of his search, but was among the ships launched in that timeframe. (TNG: "Up The Long Ladder")
The name of this ship appeared on an okudagram that appeared on Picard's desk monitor, and was not verbally referenced on screen. A legible version of the okudagram appeared in the reference book, Star Trek: The Next Generation - The Continuing Mission.
Buckaroo Banzai, BBI, John Whorfin, and Planet 10 (DIM 8) are all references to 1984's The Adventures of Buckaroo Banzai Across the Eighth Dimension!, a frequent subject of okudagram in-jokes. While working at 20th Century Fox in the 1980s, Denise Okuda (née Denise Tathwell) was the director of the Buckaroo Banzai Fan Club.