Nice question, but you've got the premise a bit wrong. Roman slaves could not be called by their master's name, not ever. But freedmen were, as a matter of law/custom. This applied to all cases, and wasn't the whim or fancy of a particular nobleman. Of course to differentiate, the slave would append his old, "barbarian" name as a cognomen. So if one Marcus Gavius freed his slave Plato, then the freshly-minted freedman would be called Marcus Gavius Plato.
Anyway, the guy you have in mind is likely to be Publius Clodius Pulcher who had a notorious gang of slaves at his beck and call. Here is Plutarchus telling us about his conduct in his biography of Cicero:
 (1) But Clodius, having escaped his peril, and having
been chosen tribune [in 57 BCE], at once began to attack Cicero, arraying and
stirring up against him all things and all men alike. (2) He won the
favour of the people by benevolent laws, got large provinces voted to
each of the consuls (Macedonia to Piso, and Syria to Gabinius),
brought many of the poorer class into organized political activity,
and kept armed slaves about his person.
(7) But Clodius met him [Cicero] everywhere in the streets, with a band of bold
and insolent men about him, who made many unbridled jests upon
Cicero's change of attire, and often pelted him with mud and
stones, and so interfered with his supplications to the people.
There are also a few references to Clodius's gang in Cicero's own speeches, catalogued here.
Btw, It is instructive to note that Cicero approved of his own supporter, T. Annius Milo who had a gang of apparently the same kind but ranged in the service of the conservative party - in Cicero's telling it sounds like a high-minded civic organization....
Gaius Lucius is an impossible name. Lucius is a prenomen (sort of given name) and so is Gaius.
Welcome and +1 for the question.