Antony came from Denver, Colorado and was part of the Hangdogs tribe, before Caesar's Legion invaded. The Hangdogs tribe resisted the Legion's efforts to take over the tribe and integrate it into the Legion. Caesar's Legion took over the tribe by throwing the tribe's dogs onto a fire, forcing the Hangdogs to surrender. Antony, after the integration of the tribe, became a Houndmaster.
During the quest Nothin' But a Hound Dog, if you order Rex to stay and you approach Antony you will get the same special dialogue if you had him by your side.
Behind the scenes
His name is likely a reference to real-world Marc Antony, Julius Caesar's right-hand man and an eventual avenger of his assassination. Historically, Antony was Caesar's Master of the Horse, or primary lieutenant, during Caesar's dictatorship in Rome. After this, he fought against Octavian for the throne in Rome. The in-game character refers to himself as a Master of the hounds.