Kurenai backstory:
Age: 27
Graduated: age 9
Chuunin'd: age 13
Jounin'd: age 27

genjutsu specialist
Best in Konoha
STR + CON below average.
DEX, INT, WIS high
CHA ave.

Mission record:
S:14
A:138
B:235
C:158
D:152

Unusually high ratio of B and C-rank to D-rank for her time spent at her respective military rank suggests frequent military action early in her career. (Consistent with her age: She would have become a genin during the Third War) The Third War was also ongoing when she became a chuunin, perhaps she earned a battlefield promotion or, similarly, was honored for acting above and beyond/displaying chuunin qualities in a combat situation?
Relatively high number of successful S and A-rank for a fresh jounin suggests exceptional skill and dedication.

Shown by her interactions with her genin (She is the Team Mom) to be caring, thoughtful and un-malicious, bordering on YN. Since her hobby is evening drinks, might that imply acquaintance or possible friendship with others who do so, like Anko? Similar age suggests peers in Academy. Possibly friendship post- or peri-wartime. Did they have to work together at some point?


Names in the Narutoverse are typically puns, occasionally related to character personality.
Yuuhi = Evening Sun
Kurenai = Crimson (NB:Kanji can also be read as "beni", a traditional lipstick)

Yuuhi suggests an evening person, not an early riser or at least, not a gracious one. That it means "evening sun" while Hinata's means (roughly) "A place facing towards the sun" may be indicative of their relationship(that Hinata looks up to her as a surrogate mother figure), as well as that Kurenai may have shared personality traits with Hinata when younger.
That it is the "evening" sun is telling as well: the last few moments of light as the sun rails against the encroaching dark. Coupled with her mission record, suggests a strong sense of dedication/determination. (even in the face of the inevitable?)

Kurenai or "crimson" brings to mind an image of blood or bloodstains, suggesting some kind of disaster or similar misfortune in her past. Or is the misfortune in question the death of her lover Asuma, which would mean that Kishi had been planning that since he first introduced the idea that the two of them were involved. Or possibly both, and she is seemingly plagued by misfortune in life?
Conversely, when taken in conjunction with her name Yuuhi it brings to mind an old rhyme foretelling good fortune at sea. Perhaps she enjoys swimming or hot springs?
That her name can also be read to mean a traditional form of cosmetics suggests that she has skill in infiltration and/or court etiquette: she may have experience as a spy or an ambassador to other villages. Once again, when read in conjunction with the name Yuuhi, it calls to mind an image of a woman with a painted mask in the evening light. Does she have a sense of the romantic, or merely DID she? Would she perhaps enjoy romantic novels, in contrast to Kakashi's love of porn? Or was that sense of the romantic destroyed in whatever misfortune she may have endured in early life (If there was some)?