The Ferengi captain in “The Battle” is DaiMon Bok, usually called Bok.
Bok commands the Ferengi vessel that approaches the Enterprise-D and requests a meeting with Captain Picard. He presents Picard with the USS Stargazer, Picard’s former command, claiming it as a gift to the “hero of Maxia.” The gesture conceals Bok’s real motive: revenge for the death of his son during the Battle of Maxia.
Bok uses a mind-affecting device called an orb to make Picard relive the earlier battle and believe the Enterprise is attacking him. The plan nearly turns Picard against his current crew, but Riker and Data uncover the deception. Bok’s first officer, Kazago, later reveals that the orb is forbidden and informs Riker that Bok has been relieved of command.
Brunt and Zek are important Ferengi characters from other Star Trek stories, while Tog is associated with a different Ferengi episode. None is the captain in “The Battle.”