I went digging around, and found the root bri- means "short/brief", and seis is a version of seus which comes from sōs, meaning "safety/rescue." So the name could mean "brief safety," possibly referring to how Briseis was captured by Achilles, which led to a brief period of peace before war quickly broke out again because of her.
My name is Briseida. I was told once that the name meant "Beautiful Cheeks" but this website doesn't know the meaning. My family and friends call me Brisy or Bri. I wish I knew the true meaning of my name.
It is a cool name, but it appears in the Iliad as Achilles' "prized woman"'s name. He won her in a battle, as women were treated as loot in that time period. As much as I want to love it, I've studied the Iliad too closely to be comfortable naming a girl, who I would hope to be strong and assertive, this.
― Anonymous User 12/23/2015
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There's something truly fascinating about this name: classic yet refreshing. The succession of sounds reminds me of a warm summer breeze. And the fact that this name occured in the Iliad makes it even more beautiful!
I think Briseis could be a really cool and beautiful name on a girl, but I can only picture it on someone young. I have a hard time picturing a middle aged woman named Briseis.