Why was it important to know the nationality of a slave in the Roman world?
This is a great question. According to Roman law, the nationality of a slave had to mentioned before the sale of any slave. In fact, according to the edit of the Aedile (the Roman official who controlled the markets), four elements had to be divulged to potential buyers of slaves: origin, physical condition, age, and price.
All of these are common sense to us, except perhaps the origin or nationality. Nationality was important in the ancient world, because the ancient world assumed that certain nation were better at certain tasks than other nations. In other words, Romans believed that there were national characteristics. Here is a quote from the Digest:
“It is assumed that some slaves are good, because they come from a people (natio) which does not have a bad reputation, and others are thought to be bad because they come from a people which has a rather bad name.” (Digest 184.108.40.206)
If you also read Roman texts that deal with slavery, they write pretty much the same thing. I will also link Orlando Patterson's book, Slavery and Social Death.