I've always said it coz-EEM-uh but I'm not really sure. I like it though I don't think I'm brave enough to ever use it.
It's an Italian name so it's pronounced "KAW-zee-muh".
I've always said it 'coss-EE-ma'. But Forvo says 'cozzy-ma'.
Cosima is a name that I recently found out I was pronouncing wrong. It is Ka seema.
It is pretty and exotic, but you would probably have issues with it.