Did Zeus'/Iupiters' lightning bolt ever attain it's own personal name, or did the Greeks and Romans only ever use generic words for thunder and lightning?
Zeus didn't have a single individual weapon, like Þor's Mjǫllnir, which would come back to him after each strike—instead, most depictions have him hurling a new lightning bolt each time, which is destroyed on impact. So in that sense, there was never a single bolt to name.
However, in Ancient Greek, there are several words for what happens during a storm: brontë for "thunder" and astrapë for "lightning" are extremely common. Most often, Zeus's weapon is neither of these: it's keraunos, a "thunderbolt". This is a somewhat poetic word that's especially associated with Zeus throwing down Cyclops-crafted bolts.
In Latin, the distinction is less pronounced, but fulgur or fulgor is conventionally "lightning" in the general sense while a fulmen is a "thunderbolt", an individual strike, especially one hurled by Jupiter. The words are mostly interchangeable, but some authors draw a distinction between them (possibly after the model of Greek). In metaphorical usage, fulgur is generally about brightness and flashing, while fulmen is about destructive power.