A few Roman emperors are commonly known by nicknames. I'm thinking specifically of the Emperors Gaius (Caligula) and Antoninus (Caracalla.) These nicknames were never in official use, at least while they were alive. However, they seem to be by far the most commonly used names for said emperors today.
My question is whether the use of these nicknames after the deaths of these emperors is meant as an insult or a sign of contempt, or whether they were simply used for the sake of distinguishing one emperor from another of the same name (as with Antoninus, a name used by more than one emperor.) I ask because both of the listed emperors are widely regarded as two of the worst in Roman history. Caligula and Caracalla seemed to be used during those emperors' lives informally as agnomens, and both are based on pieces of clothing they wore. And Caligula, or "Little Boots", does seem kind of insulting or mocking as a nickname, referring as it does to the little soldier's boots that young Gaius wore while hanging around his father, the general Germanicus, while on campaign with the legions. (The implication of "Caracalla", translating as something like "Gallic cloak" supposedly based upon a style of cloak he liked to wear, is a little less clear to me.)