Official pronunciation and romanization are unknown. Her name is "冴月 麟", generally pronounced "Satsuki Rin (さつき りん)."
Her name Rin (麟) stands for the mythological creature Kirin, prompting some to believe that she was supposed to be a personification of a kirin. This is supported by the fact that by the Japanese name order, her name is "Satsuki Rin."
Based on a remark by Marisa in her Extra Stage, Rin is theorized to be a nurse, but this is pure speculation. However, in modern Japanese popular culture, the kirin is often conflated with the unicorn (cf. Final Fantasy, Monster Hunter), which has healing powers; this would suggest a connection between kirin and nurses.
From the picture, she is shown holding a musical instrument. It could be that she is actually a Tsukumogami (artifact spirit).
A Twitter post revealed the girl in the picture wasn't Rin Satsuki, and instead claimed it was a Team Shanghai Alice "poster girl".