Question

Why does the slave dealer change Northup’s name? Why would it be common practice to rename slaves after their owners?

Answer 1

The slave dealer named Theophilus Freeman changed Northup's name to Platt to take away his identity. Losing his name made Northup realize that he has lost his connection to his family and he has lost his freedom and became a slave.
Slaves were sometimes named after their owners to prevent confusion. For example: A master has a slave named Sam. Then he bought a new slave also named Sam. The new slave is then given the surname of his previous owner which might be Butler so the new slave's name became Sam Butler.

Answer 2

The slave dealer had to change Northup name since normal slaves did not have last names so, ir order to make sure people did not question if Northup was a slave, he had to change his name. It was assigned a random and indistinct name to Solomon (Platt), which took from Northup his last trace of identity, his connection to the life his family provided to him and also with the joy he use to feel when he was on his house. After that moment, he started to be known by an arbitraty name, what establish the fact that Northup finally, seemingly irrevocably, became a slave.

It was common to rename slaves after their owners after he was set free. People did that because it was not only a logical thing to do but also the easiest way to be identified. Besides that, the Government seemed to be in a hurry when it was about slaves names, since that way they were able to be registered as a person, as a citizen.