Thinking about Cassandra Cain and what the name Cain means in a biblical context.
In the Torah (I'm Jewish, so the Jewish interpretations of the text are what I'm familiar with - if any Muslims or Christians out there have different perspectives, I'd love to hear them!) Cain was a farmer, working the land to raise crops, while his brother Abel was a shepherd, raising sheep for wool and meat. They both offer sacrifices to G-d, but while Abel offers the best portion of the meat from his flock, Cain offers the worst of his crops. G-d accepts Abel's offering, but rejects Cain's. In a jealous rage, Cain kills his brother, committing the first murder and being exiled for his crime. He is destined to walk the Earth, visibly marked as an outcast, poisoning the soil he once worked in and bringing ruin to the world around him.
For Cassandra to carry this name is very interesting. It lines up perfectly with how she sees herself, especially in her earlier stories - desperately trying to please a father who she loves and fears in equal measure, until she finally does the unforgivable to earn his love. Forever tainted by a murder she committed when she was young, unable to escape it, destined to forever be an outcast from the people around her. She believes that she is a bringer of destruction, doomed to bring ruin to every life she touches; that she carries a mark upon her forehead that everyone can see, branding her forever as a murderer. She has sinned, and she can never escape that.
The blood of her victim cries out from the ground, and the mark of Cain is forever branded upon her forehead. She can never escape the curse of being eternally an outsider. She can never be clean of the blood on her hands. She can never be forgiven for what she has done.
Also thinking about the name Cassandra and what it means in the context of Greek mythology.
Kassandra (ฮฮฑฯฯฮฌฮฝฮดฯฮฑ) is fairly well known for being a seer, blessed with the gift of prophecy, but cursed so that no one would believe her. I had to go check (I used Wikipedia, but it's usually pretty accurate and comprehensive about Greek myths, since so many people know about them), since I'm not as familiar with Greek mythology as I am with the Torah, but there's a lot more there, and it's very interesting. There's a lot of material, so I'll only be including what I feel is relevant to Cassandra.
Kassandra was a princess of Troy, born to great status on the 'wrong' side of the Trojan War (at least, wrong according to Greek writers). She is a priestess of Apollo, and most versions of the myth paint him as giving her the gift of prophecy to try and get her to sleep with him, then cursing her to never be believed when she refused or changed her mind. Because of this curse, she is seen as mad, and her father Priam locks her away. Later, after the sacking of Troy, she is taken as a slave by the Greek king Agamemnon, and is brought to his home, where she and Agamemnon are murdered by his wife, Clytemnestra, in retribution for Agamemnon killing his daughter Iphigenia to allow the Greeks to sail to Troy. The murder takes place offstage, but Kassandra goes to her death willingly, driven to despair and madness by her curse.
There are a lot of very interesting parallels here. Cass is born to great status (daughter of two master assassins) on the wrong side of DC's ethical spectrum. David Cain has parallels to both Apollo and Priam. As Priam, he locks her away from the rest of the world, isolating her for something that isn't even a crime. As Apollo, he gives her what he sees as a gift, a gift of sight and knowledge that few others have, but he wants something terrible in exchange, something that she is not willing to give - Apollo wanted sex, but David Cain wanted her to kill. When she refuses, she is cursed to never be able to express herself, to be heard by those around her - that is, although she was never able to speak in her childhood, it is only after she runs away in horror at what she has done that she finds out how much of a handicap that is. Only after she refuses the most powerful man in her life does she realize that he has cursed her. Later, after she is taken in by another man (Bruce doesn't have many parallels to Agamemnon, but he does serve a similar purpose of decisively separating her from her past), she is killed by Shiva, who has some very interesting parallels to Clytemnestra. While Shiva is Cassandra's mother, not her - I don't know the correct term for Kassandra's relationship to Clytemnestra, but it's not the same - she is not a very present mother. Shiva gave her to David Cain at birth, and they don't meet again until Cassandra is a teenager or young adult, depending on the continuity, so they are essentially strangers, tied together by a bond neither of them asked for. In a way, Shiva's relationship to her sister Carolyn (killed by David Cain to 'help her reach her true potential') parallels Clytemnestra's relationship to Iphigenia. They are both broken by the deaths of these women they loved, women who were killed by a man in service of a 'noble' goal. They would not be murderers without these deaths in their pasts. And Clytemnestra kills Kassandra to avenge Iphigenia (not that Kassandra had anything to do with that, but she was associated with the man who did, which Clytemnestra saw as crime enough), while my reading of Shiva's death wish is that she wants to make Carolyn's death worth something - if Carolyn died to make her what she is today, then she owes it to her sister to be a legend, and that means dying in a blaze of glory, not growing old and fading away. So Clytemnestra kills Kassandra for Iphigenia, and in a twisted way, Shiva kills Cassandra for Carolyn. And just like Kassandra, Cassandra sees her death coming and goes to meet it willingly.
Okay, so @aingeal98 got me thinking about where Cassandra's names come from in-universe, and I have enough thoughts about it that I want to tack them on here.
First, the name Cain. As aingeal pointed out, unlike the biblical Cain, Cass wasn't given the mark that branded her as a murderer by a higher power; she was given it by her father. Cassandra's Mark of Cain is her name, and David Cain held that name first. He was the one who taught her to kill, who made killing everything she knew, and he was the one who called her his daughter and passed down his name to her.
Except, in a way, she did get her name from a higher power.
It's not an accident that I compared David Cain to both the Jewish G-d and the Greek Apollo. When Cass was a child, I think her father very much was a g-d in in her life. He was one of the only people she saw, and definitely the only one she saw consistently. He controlled everything about her life - what she ate, when she slept, what she wore, what she knew. He punished her when she displeased him, and probably rewarded her when she did well (off the top of my head, I can't think of any on-panel instances of him rewarding her, but it makes sense for him to use both positive and negative reinforcement).
In some ways, her running away is more like someone breaking from religion than breaking from family. She is only able to leave because her worldview is entirely changed by her horror and guilt. It reminds me of the way some people will be fully devoted theists until they find out something about their religion or their specific synagogue/church/mosque/etc. that completely breaks their faith. And it leaves her in a similar position to many people who escape cults/high control religions: alone, afraid, without material resources, and struggling to comprehend a world utterly different from the one they know.
That near-worship, that deification, was very much part of my thoughts when I was talking about David Cain's parallels with the Jewish G-d or the Greek Apollo.
As for the name Cassandra, this one's a bit simpler, but still very important. This name was given to her by Barbara Gordon, the Oracle. In Greek mythology, Apollo was associated with all knowledge of the future, and was the one to give Kassandra her gift and then her curse. Although I'd say David Cain (the most powerful man in Cassandra's life, and the one to give her the gift of sight and the curse of being unable to share it), still has stronger parallels with Apollo than Barbara does, it's very much worth noting that Kassandra is an oracle. If I recall correctly, that connection is even highlighted in the comics by Babs. For Cass to be named after a famous Greek oracle by the Oracle of Gotham is no accident.