Byzantion was razed to the ground for supporting Septimius Severus' opponent Pescennius Niger in the Year of the Five Emperors (193 CE). When Severus visited Byzantion years after, he decided to rebuild the city, including the baths of Zeuxippos.
The origin of the name of the baths varies per author.
According to Hesychius (6th century), it was because it was located close to the altar of Zeus Hippios, which was the grove of Herakles who tamed the horses of Diomedes (hence the name 'Zeuxippos').
Lydus (6th century, contemporary of Hesychius) recounts the origin of the bath after describing its damage in the Nika riot of 532. He claims that the forum also bore the name Zeuxippus, after King Zeuxippus who led the Megarians to Byzantion. He contrasts the name Zeuxippos of the Forum to that of Severus ("...a commander of the Romans"). Instead of referring to the destruction of Byzantion as a consequence of the civil war with Niger, Lydus claims Severus built the bath during the war for himself as he struggled with "an illness of the joints".
According to Malalas (6th century), it was named after a bronze statue of Helios in the middle of the Tetrastoon. The statue carried an inscription 'To the horse-yoking (Zeuxippos) god'. These details are copied in the Chronicon Paschale (7th century).
According to the Suida (10th century), Severus expropriated property to build the Hippodrome. The Zeuxippos baths were built in the temple of Zeus.
Lydus (6th century), Chronicon Paschale (7th century) and the Parastaseis Syntomoi Chronikai (8th century) all maintain that the baths bore the name of Severus, its original founder.