I'd originally asked this on SE:H, but it was suggested that here would be more appropriate.
Triggered by recently reading about the history of English names with Anglo-Saxon roots and the development of diminutive forms, I'd started wondering:
What do we know about hypocorism/diminutive name forms in Latin names in Roman antiquity? Or to use a modern analogue, if friends and family call William and Harold, Will (or even Willie?) and Harry, then did friends and family of Romans like Julius Caesar, in private, use forms like (pure speculation here) ... cull for Caius -> Caiulus -> cullus -> cull.
Note, I'm not talking about "nicknames" here, known in Roman times as cognomen, so not names like cicero, niger, ahenobarbus, etc.
As per Wikipedia
A hypocorism, from Ancient Greek ὑποκόρισμα (hypokorisma), from ὑποκορίζεσθαι (hypokorizesthai), meaning 'to use child-talk' is a diminutive form of a name. Hypocorisms include pet names or calling names, often a, diminutive or augmentative form of a word or given name when used as a nickname or term of endearment
I tried doing some research, first into given names in Latin, of which lists are plentiful. We're all familiar with Marcus, Lucius, Caius, Claudia, and so on.
Then reading up on diminutive word forms in Latin. Many will know about the -ulus/-ula forms, but this interesting link lists others used in the language: The Formation of Latin Diminutives of Nouns and Adjectives
On English names the article Behind the Name – Diminutive explains
A diminutive (or pet name) of a given name is a short and/or affectionate form. Often they are only used by friends and relatives.
The most common diminutives (at least among English names) are those that are short forms of the original name, very often from the first syllable or sound of the name. For example, Alex is from Alexander, Barb is from Barbara, Deb is from Deborah, and Mike is from Michael. Other short forms don't come from the beginning of the name, but instead from the end or the middle, like Beth from Elizabeth, Fred from Alfred, Greta from Margareta, and Lisa from Elisabeth.
But nowhere could I find anything that would show pet names used in ancient Rome. Did Romans really always use the full given name, and maybe with the Latin diminutive form? The link above states that -ill- and -tt-
[are] found used only with feminine names, but it could theoretically also be used with others words, e.g. a masculine form of Līvilla would be Līvillus.
So, Caesar's mum called him Caius and maybe Caiulus, but no known pet name form of Caius? Was Marcus Ulpius Traianus never called Marc (or at least the appellative form Marce?) Seeing as how Romans abbreviated inscriptions, could we end up with M.Ulp.Trai. as Mulpe among very close friends or at least before Trajan was raised to office and emperorship?
The detailed Wiki article on Roman naming conventions makes note that
Roman men were usually known by their praenomina to members of their family and household, clientes and close friends; but outside of this circle, they might be called by their nomen, cognomen, or any combination of praenomen, nomen, and cognomen that was sufficient to distinguish them from other men with similar names. In the literature of the Republic, and on all formal occasions, such as when a senator was called upon to speak, it was customary to address a citizen by praenomen and nomen; or, if this were insufficient to distinguish him from other members of the gens, by praenomen and cognomen.
and on the cognomen
Unlike the nomen, which was passed down unchanged from father to son, cognomina could appear and disappear almost at will. They were not normally chosen by the persons who bore them, but were earned or bestowed by others, which may account for the wide variety of unflattering names that were used as cognomina. Doubtless some cognomina were used ironically, while others continued in use largely because, whatever their origin, they were useful for distinguishing among individuals and between branches of large families. New cognomina were coined and came into fashion throughout Roman history.
But while the former indicates that there was Marcus but no Marc, the latter (with my emphasis) indicates that it's unlikely even his closest friends and family (such as they were) would have called Nero... well, Nero to his face!
Are there no Latin hypocoric name forms similar to William -> Bill, Richard -> Dick, Ann -> Nancy, Helen -> Nellie?