If there were slaves with classical names, it would have been nothing unusual. Consider that when Joel Chandler Harris named his famous narrator--a kindly, folksy, former slave--Harris chose the name Uncle Remus. There are slave narratives written by Lucius Henry Holsey and Octavia V. Rogers Albert. This will mentions slaves with the names Caesar, Bacchus, and Pallas, while this will mentions slaves named Cato and Antony. Here's a slave named Augustus and two slaves named Zeno. Using the slaves names index, I've confirmed multiple slaves named Julius, Brutus, Pompey, Scipio, Junius, Claudius, Cornelius, and one real Remus.
Free or slave, classical names were just much more common in the 19th century: Aside from Cassius Marcellus Clay, we have the politicians
Brutus Junius Clay, Julius Caesar Alford, Augustus Porter, Pompey Strickland, Marcus Weyland Beck, Lucius Lyon, Caesar Rodney, Theodorus Bailey, Horace Mann, and
Similarly, we have moguls like Junius Spencer Morgan and Cornelius Vanderbilt and military men like Horatio Gates, Ulysses S. Grant, and Sylvanus Thayer. And finally, we have the not-so-famous Flavius Josephus Ballou.
Departing from the Roman theme, we have the still-classical Hannibal Hamlin, Cyrus Hamlin, Darius Couch, and Lysander Cutler. Names like Homer, Anthony, and Alexander were also quite popular at the time.