The Captain has gone by many names, by many historians. However, most final historical records indicate that the key figure in the defeat of the Hierarchy was a Human named Zelnick. [In the first release of Star Control II, there was no default name; the first act in a new game was to name the commander and the flagship. The later released 3DO version named the captain Zelnick and the flagship the Vindicator.]
Zelnick was born on the the colony world of Unzervalt in the Vela system, and showed an unusual aptitude for communicating with Precursor computer systems, including the mainframe computer operating the factory that produced the Vindicator. After Captain I. Burton was killed in a Slylandro Probe attack, he took control of the Unzervalt mission and piloted the Vindicator from Unzervalt back to Earth, and is generally agreed to have played a pivotal role in the events of the quadrant from 2154-2159.
Full details on The Captain are sketchy. Only one known image, taken during his recovery after escaping the destruction of the Sa-Matra is available of Zelnick during his time as a captain. From it, and from knowledge of the history of Unzervalt itself, we can conclude that Zelnick was Human, male, probably Caucasian, and under 20 Earth years old at the beginning of his mission.
He is one of the most legendary humans ever to travel the stars.