This name was used by Shakespeare (who got it from Plutarch) in Antony and Cleopatra for one of the attendants of the Egyptian queen. An interesting possibility, it is heard occasionally in the UK, even less frequently in the US.
The Shakespearean pronunciation: CAR-mee-un (like Carmen) or CHAR-mee-un (like the word "charming")
Charmian Stroud, character in AgathaChristie's 1944 short story Strange Jest (a Miss Marple mystery)
Charmian Brown, "Lady Sophia Sefton in disguise" in Jeffery Farnol's bestseller The Broad Highway (1910)