"Abraham" means father of multitudes (Genesis 17:5). His name was changed in keeping with God's promise to make him the "father of multitudes". "Sarah" means "mother of nations" (Genesis 17:15) probably for a similar reason. The name change corresponds to a change of identity. Even Jacob's ("supplanter") name is changed to Israel ("one who struggles with God"). Oftentimes, people in the Bible give names based on what they experienced in their time, God gave names based on His covenant promises that would be fulfilled in the future.
Sarah must have gotten this slave during their sojourn in Egypt during the famine:
But she had an Egyptian slave named Hagar (Genesis 16:1).
The slave likely had no say in being conjugally given to Abram:
Go, sleep with my slave; perhaps I can build a family through her (Genesis 16:2).
Even though now a wife, she was still treated a slave, for Abram permitted Sarah to mistreat her as she pleased:
“Your slave is in your hands,” Abram said. “Do with her whatever you think best.” Then Sarai mistreated Hagar; so she fled from her (Genesis 16:6).
Sometimes, as we read these accounts, we simply gloss over what might normally produce in us moral indignation. We do not normally embrace slavery without protest, yet here Sarai has taken Hagar as a slave. We normally do not consider it moral to have conjugal relations with anyone other than one's own wife. We normally do not consider it right to force anyone into conjugal relations, which appears to have been the case with Hagar. We normally do not consider it moral to mistreat one's wife, which Hagar became (Genesis 16:3). And the collusion between Abram and Sarai to jointly agree to allow this makes this even more nefarious. Did you miss all that in reading the first six verses of Genesis 16? I did... until today.
Now, consider Israel's four-hundred-year slavery to Egypt, where the descendants of Abram and Sarai were mistreated by the Egyptians. I'm not saying one thing led to the other or that God was punishing Israel in Egypt because Abram and Sarai enslaved and mistreated an Egyptian. However, I find it somewhat ironic, perhaps a kind of poetic justice, a "what goes around comes around." Of course dramatic irony is a literary device but whose to say it is not also a pedagogical tool, even one to teach the Golden Rule, namely, "Do to others as you would have them do to you" (Matthew 7:12; Luke 6:31).