As slaves, African Americans had considerable latitude to choose their own names. In the 17th and 18th centuries, American masters would often make an attempt to give new names to newly-purchased slaves, but they didn't always stick. Many slaves retained the names they had received in Africa, or the Western names they may have received in the Caribbean or elsewhere. Many masters had no problem with this. When slaves were baptized, they sometimes replaced their African name with a Christian one, but this wasn't a hard rule either. Many slaves had two or more names. Hence, you had people with names like "Billy Congo" or "John Quash," which over time could become surnames.

The children of enslaved men and women were named by their parents. It was very common for children to be named after parents, grandparents, uncles and aunts, and other relatives. This meant that on any large, stable plantation in the late 18th or early 19th century, you would find many slaves with the same names. This could get confusing, so some slaves acquired surnames in order to distinguish themselves, based on occupation ("Cooper Joe"), skin color ("Black Joe"), place of origin (like "Jack Gambia" or "John Gola"), or something else. Over time these could also turn into surnames.

Other slaves took surnames for themselves simply because they felt like it. It gave them a greater sense of freedom and independence. Some took on the name of a former owner, because of its connection with their own families and history. (Almost none named themselves after their current owner.) Others just gave themselves names that sounded cool--George America, John Twopence, James Traveller, John Freeman.

At the turn of the 19th century, these surnames were still pretty rare; about one in 100 in the Lower South, and one in ten in the Chesapeake. As the 19th century progressed, it seems to have become more common, but I'm not sure about this. At any rate, these practices give you a sense of how names were acquired at emancipation. They gave themselves names which tied them to their family, history, identity, occupation, or whatever they felt like.