I always pronounced it COSS-im-ma until I started watching this (super amazing) tv show called Orphan Black, where one of the characters is called Cosima. They say coss-SEE-ma on the show, so now I instinctively pronounce it like that.
I definitely think it's useable. It's a really, really nice name. It's kind of understated fancy. Fun fact: it's the name of Nigella Lawson's daughter.
I don't really like the name Faith, but it fits nicely with Cosima in terms of sound. Some other suggestions:
Cosima Violet
Cosima Belle
Cosima Rose
Cosima Lillian
Cosima Beth
Cosima Valerie
Cosima Autumn
Cosima Freya
Cosima Calla
Cosima Isobel
Cosima Penelope
Cosima Laura
Cosima Olivia
Cosima Florence
Cosima Poppy
Cosima Fawn
Cosima Edith
Cosima Matilda
Cosima Vivienne
Cosima Diana
Cosima Gigi
Cosima Ursula
Cosima Edeline
Cosima Claire
Cosima Ivy
Cosima Helena
Cosima Leanna
Cosima Aria
Cosima Beatrice
Cosima Lyla