A pseudonym (literally, “false name”) is a name that a person (or, sometimes, a group) assumes for a particular purpose and that differs from his or her original orthonym (or “true name”) (Wikipedia).
Anonymity is derived from the Greek word ἀνωνυμία, anonymia, meaning “without a name” or “namelessness”. In colloquial use, anonymity typically refers to the state of an individual’s personal identity, or personally identifiable information, being publicly unknown (Wikipedia).
So what’s the Bauta? An anonymity or pseudonymity device? From my point of views, assuming a predefined and generic role like the one of Signora Maschera means staying anonymous.