He was taken into the family, when only a few weeks of age. His name being that of my own, mine was changed, for the purpose of giving precedence to his, though I was his senior by ten or twelve years.
Having his name changed is taking away his identity, which is partly what slavery is. The white child gets precedence over the slave, even if it's just a name.
He was considered the most valuable and able-bodied slave on the plantation; but no matter how good or useful a slave may be, he seldom escapes the lash.
This line shows the true brutality with slavery. Even a well-liked slave, who did "right" still gets the lash just because of their color.
It is not for a single generation alone, numbering three millions—sublime as would be that effort—that we are working. It is for humanity, the wide world over, not only now, but for all coming time, and all future generations:—
This suggests that the efforts of the narrator are not to just benefit this generation alone, but for all future ones to come.