What's in a name?
Kirigakure- Japanese, meaning "hidden mist". It's possible she gave herself this name, as she fights using a style of the same name and she was more than likely an orphan from a young age.
Shura- "Carnage" or "bloodshed" in Japanese. ALTERNATELY Arabic, meaning "consultation", or a method of decision-making in traditional Islamic societies.
Headcanon
-Was a scrappy, angry, foul-mouthed kid for a long while even after Shirou found her. He had to re-teach her how to be human.
-Shirou also gave her a birth date since she was living like a wild animal and didn't have one. He chose 08/08 because it's easy to remember
-Had a very intense rivalry with Arthur growing up
-Has had more than a few near-death experiences
-Very good at surviving, both from Exorcist training and her experiences as a kid
-Looooooooves alcohol, not just for the effects but the taste as well
-Not all that interested in/hung up about sex! It's a thing people do and sometimes she does it too; whatev's
-On that note she is straight with the occasional exception. Canonly she likes "cool headed" men but I can see loudmouths catching her interest as well.
-Is very in tune with her body. It's both a carrying case for swords and a weapon in and of itself, in addition to being very distinctly hers. This is part of why she's so comfortable with dressing as she does. The other reasons are of course that it makes fighting easier, and she gets hot really easily
-Thinks formalities are a bother and a bore
-Genuinely loves her job. Unfortunately she's brilliant and thus easily bored, which can make her motivation plummet to levels of laziness and loud complaints
-Very rarely gets sick! But when she does it hits her like a bulldozer
-Had no female classmates, but she didn't much care
-Pacifist at heart! (Thanks, Shirou.) She'll fight and might even enjoy the challenge, but what she really loves about being an Exorcist is helping others
-Not ashamed to cry or be seen crying. It's part of the Exorcist "philosophy" of not bottling up emotions
-She wants Rin to be a good exorcist, so she can justify what Shirou did, and justify caring for him
-Doesn't trust Mephisto, but does enjoy his company (they play video games together a lot). Her friendliness towards him is in part from this, and in part from the old adage "keep your friends close, and your enemies closer."
-She's ridiculously observant in canon about demons and the like because she can smell/taste them, as a snake would