Emperor Valens built the baths and named them respectively after his daughters Anastasia and Carosia. They are also attested in the Notitia Urbis Constantinopolitanae.
One source, Ammianus Marcellinus, claims that the bath was named after another Anastasia (Constantine's half-sister, wife of Bassianus Caesar, c. 314). Ammianus also reports that the two legions that supported the usurper Procopius were stationed here when the latter declared himself emperor and took control of the city in 365.