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.
Zeus' thunderbolt in ancient times was often depicted as a single weapon. It was usually depicted as a winged flaming staff with lightning wrapped around it (although the lighting then was different from the zig zag we use today, it's got more right angles). You can see this in the heraldry of the Roman legions and into the Middle Ages in heraldry. Here's a decent drawing of how it was depicted: https://mistholme.com/dictionary/thunderbolt/