After watching "Caligula with Mary Beard" (BBC documentary), I wondered if his nickname was used during his lifetime. And if it was, do we have an idea on its popularity ?
I'm under the impression most of the sources we have are heavily biased against him. Was the nickname only used by his oppenents and did the surname stick because a bias in the source ? Or was it a popular way of naming the emperor amongst the population ?
Caligula's father was a prominent Roman general called Germanicus, and Caligula spent a significant part of his childhood with his family in legionary camps while his father was off campaigning.
As a toddler, he got outfitted with a cute little soldier outfit, which the soldiers found amusing, and the nickname Caligula is derived from the caliga, which was the leather sandal soldiers wore and would have been part of the child Caligula's little outfit.
So the nickname that we know the emperor as today would have been more endearing than mocking, and it's worth noting that when Caligula first came to power, he was initially hailed with excitement. The Roman people had been jaded by the purges of his predecessor Tiberius, and Caligula's father (who many suspected had been killed under Tiberius's orders) was an extremely popular war hero. So when we first got to Rome as emperor, he was greeted with several affectionate nicknames such as "shining star", "little chick", "dear child", as well as Caligula. It took a while before his reputation as an unstable sociopath had a chance to develop.
With all that being said, Caligula was just a nickname, and it would never have been used in any formal setting, or to the emperor's face. Contemporary sources uniformly refer to him as "Gaius", which was his given name (Gaius Julius Caesar).
The Twelve Caesars (p. 157 & 165 address his nicknames)