Did American slave holders typically give their slaves the names of Roman nobility?

Even if as some have said giving slaves Ancient Greek and Roman names could be ironic it is surely also a sign of the immense educational and cultural role and prestige of Greek and Latin languages and literature (including history, rhetoric and philosophy as well as imaginative literature) for most educated people of the eighteenth and early to mid nineteenth centuries.

Because such study is vastly less common today we almost certainly often miss the extent to which politicians, writers, judges and even journalists of those days had in mind and were influenced by ideas taken from the Classical World. Hence e.g. newspapers founded in the nineteenth century with 'Tribune' in their title assumed that their potential readers knew enough about the Roman Tribunus Plebis to understand that the role of a 'Tribune' was to defend the interests of the common people.

If you read the Wikipedia article on the white American Cassuis Marcellus Clay (who was himself named after a champion of the Roman Republic and of the liberty of its citizens) was a heroic figure. He was more than once wounded by would be assassins who objected to his opposition to slavery, whom he more than once fought to the death, in more dangerous fights even than a heavy weight boxer has to face.

Even if the boxer Mohammad Ali would have preferred to be named after say a black opponent of slavery than a white one, it made no rational sense at all to take the name Mohammad Ali, the name of a nineteenth century Egyptian ruler who made aggressive war on and enslaved black Sudanese. To quote from the Wikipedia article on 'Mohammad Ali of Egypt':

“After 1823, Muhammad Ali's priority was to reduce the cost of garrisoning Sudan, where 10,000 Egyptian infantry and 9,000 cavalry were committed. The Egyptians made increasing use of enslaved Sudanese soldiers to maintain their rule, and relied very heavily on them. A more or less official ratio was established, requiring that Sudan provide 3,000 slaves for every 1,000 soldiers sent to subjugate it. This ratio could not be achieved however because the death rate of slaves delivered to Aswan was so high…

Despite the overall failure to create slave armies in Egypt at any great scale, the use of Sudanese in agriculture did become fairly common under Muhammad Ali and his successors. Agricultural slavery was virtually unknown in Egypt at this time, but the rapid expansion of extensive farming under Muhammad Ali and later, the world surge in the price of cotton caused by the American Civil War, were factors creating conditions favourable to the deployment of unfree labour. The slaves worked primarily on estates owned by Muhammad Ali and members of his family.”

Cassius Clay was not a name "given" to slaves; it was the name of a famous abolitionist, in whose honor the subject's father was named. The boxer was his son, hence Cassius Clay, Jr.

"Muhammad Ali", as he preferred, considered his birth name a "slave name" because it was the type of name which ex-slaves adopted.

The original Cassius Clay and his brother, Brutus Clay, were prominent citizens of Kentucky named for two of the conspirators who assassinated the Roman dictator, Julius Caesar. These were Gaius Cassius Longinus and his nephew Marcus Junius Brutus. The choice of these names probably reflected a hatred of tyranny and dictatorship on the part of their father, a man named Green Clay.

To answer the question given in the title, classical names were given by masters to slaves from the very beginning of the slave trade. Beginning in the 1960s this was seen as a degrading history which led some African-Americans to change their names away from classical names. Although Muhammad Ali himself got his classical name from an abolitionist, it is true that classical names were often given for degrading reasons. Remarking on this awareness in 1977, a historian wrote:

If, as has often been suggested, owners frequently bestowed classical names upon slaves, their near absence at the emancipation would mean that significant numbers of blacks rejected such public designations ...

Herbert George Gutman. The Black family in slavery and freedom, 1750-1925. Pantheon Books, 1976.

(Other writers dispute how common such rejections were in the 19th century.)

In any case, here is a full history of the practice. (Copied from another question which I regard as very similar, though that question involves other aspects of naming)

Classical names abound in eighteenth-century slave records. Even though slaves were not, as a rule, given new namess until sold to their new owners, the few instances of slave traders or sailors naming their cargo before they even reached America indicate that these chained Africans were dubbed Caesar, Nero, or Pluto, or, as the first two names on one list of cargo, Primus and Secundus.

Inscoe, John C. “Carolina Slave Names: An Index to Acculturation.” The Journal of Southern History, vol. 49, no. 4, 1983.

These names originated from a peculiar kind of Southern wit. It is well-known among Southerners even today that the names of classical heroes were given to slaves as an ironic insult to their status as slaves. It also had the purpose of demonstrating to visitors the plantation owner's own learning.

Southerners prided themselves on their knowledge and appreciation of Græco-Roman civilization and often stressed the many similarities between it and their own society, not the least of which was the institution of slavery.

Inscoe, ibid.

Occasionally a name insulted the specific personality of the slave, but more often it created a vague Classical aura which gradually lost its degrading tone.

All but one of eight slaves named in William Yeates's 1751 will were named for Roman gods or heroes. The names of almost a third of South Carolina runaway slaves [...] were of Greek or Roman origin [...] there seems to have been little correlation between the original ancient figure and his black namesake, except for an occasional dim-witted male slave named Plato or Socrates or a sexually promiscuous girl named Venus or Aphrodite. Thus, the intent of the owner in bestowing these names would have been too subtle or tenuous for the slave to have detected anything insulting about them. Nor can one assume that all of these names were first applied by masters for satiric or condescending reasons, particularly once the practice became commonplace.

Inscoe, ibid.

The practice of having masters name slaves was widespread throughout the South.

Slave children, in fact, were often, if not usually, actually named by the master or mistress. [..] Classical names, although less numerous than certain writers on plantation life would have us think, also probably reveal the hand of the master class. Our slave list includes the following: Achilles, Augustus, Bachus, Brutus, Calypso, Cassius, Cicero [...] Scylla, Silla, Siller, Sylla.

Puckett, "Names of American Negro Slaves," in Murdock, ed., Studies in the Science of Society (New Haven, 1937), pp. 471-494.

This 1937 source claims elsewhere that classical names were also common in the white population, but this is not born out by census data.

Like place-names and day-names, classical names were rarely found among the slaveholders. These names were associated almost exclusively with slaves. Prior to 1800, classical names accounted for about 20 percent of names given to male slaves born on the Ball plantation. During the nineteenth century, the share of classical names declined to about 10 percent.

Cody, Cheryll Ann. “There Was No ‘Absalom’ on the Ball Plantations: Slave-Naming Practices in the South Carolina Low Country, 1720-1865.” The American Historical Review, vol. 92, no. 3, 1987, pp. 563–596.

Ulysses S. Grant (né Hiram Ulysses Grant) was born in Ohio to an originally Puritan family who probably had different ideas about naming; the 1937 source observes that the prominence of the name Ulysses probably derives from him, not from antebellum names.

20th century historians remark on the classical interests of slave owners, but 21st century historians have been unable to avoid noticing the inherent cruelty in assigning someone a name that serves as a source of fun. They also observe that the names tend to play on skin color, either through reference to ancient Africans, or through juxtaposition.

"Such names functioned as cruel jokes: for instance, Scipio, a common male slave name, referred to the Roman general Publius Cornelius Scipio Africanus, whose agnomen, Africanus, meant “the African,” in praise of his triumphs in battle in North Africa." (Abel, Tyson, and Palsson, 2019. "From Enslavement to Emancipation: Naming Practices in the Danish West Indies." Comparative Studies in Society and History, 61(2), pp.332-365.)

"Such names served to reinforce the idea of Africans as embodiments of exotic alterity, but also invited pointed comparison between the appearance and circumstances of the slave and the illustrious personage referenced by his name. These were names to call as a joke, names whose grandiosity humiliated: Ignatius Sancho, Gustavus Vassa, Julius Soubise." (Susan Benson, "Injurious names: naming, disavowal, and recuperation in contexts of slavery and emancipation." Vom Bruck and Barbara Bodenhorn, eds. The anthropology of names and naming. Cambridge: Cambridge University Press, 2006.)

"[The literate slave trader] chose not to speak of Venus, the other dead girl. The pet name licensed debauchery and made it sound agreeable." (Saidiya Hartman, Lose your mother: A journey along the Atlantic slave route. Macmillan, 2008.)

There was nothing unusual about slaves with classical names. Julius Caesar Chappelle was born into slavery in South Carolina before going on to serve in the MA state legislature. 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. Thomas Jefferson had a slave named Jupiter. Using the slaves names index, I've confirmed multiple slaves named Julius, Brutus, Pompey, Scipio, Junius, Claudius, Cornelius, and one Remus. Consider that when Joel Chandler Harris named his famous narrator--a kindly, folksy, former slave--Harris chose the name Uncle Remus.

Why name slaves after Roman gods and nobility? 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 Rufus King.

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.

This is a massive case of historical irony and ignorance or worse from Ali

Muhammad Ali changed his name from what he called his 'slave name' Cassius Clay when he converted to Islam, the religion that sold his ancestors into slavery from Africa. He got his name 'Cassius Clay' because his Christian father was given the name in honor of the Caucasian man who freed his great grand father from slavery (the historical Cassius Clay also got many other slaves free and advanced the rights of African Americans in many areas)

So Cassius Clay was not just a free name, but the name of man who freed his slaves chosen in honour