In response to the "how long ago did it start," there are many examples of enslaved Africans and African Americans given classical Roman (and sometimes Greek) names in colonial America. So I would say it began in the 1600s. A intentional allusion in a literary example, in Aphra Behn's 1688 story Oroonoko, the titular African prince is renamed Caesar by his white captors. But real examples are also very common. From one small article you might be interested in, Slave names in Colonial South Carolina:

In addition to the slave names based upon African nominal folkways, several other naming patterns are revealed in the advertisements for runaways in the Gazette... A second category consists of names of classical, predominantly Latin, origin. These include mythological personages, such as Achilles, Ajax, Apollo, Bacchus, Cupid, Daphne, Hector, Hercules, Juno, Jupiter, Neptune, Phoebe, and Venus; historical figures, such as Agrippa, Brutus, Cato, Caesar, Nero, Pompey, and Titus; and such neoclassical favorites as Amoretta, Belinda, Clarinda, Myrtilla, Philander, Philis, Sabina, and Strephon...

Of course, you can think of the Revolutionary War-famous Cato owned by the Irish-born Hercules Mulligan (of Hamilton musical fame) to see that these names were not restricted to enslaved African Americans.

I also tried to check some slave ship manifests, here's an example from the 1830s where they are obviously not the most common, but you can see Antony, Caesar, Venus, and Homer represented. Another features a Phoebe and a Scipio.