Oli is correct: There's no mention of her first name in the novel or in the theatrical releases of GF and II. In a deleted scene from GF, Bonasera, after getting the call from Hagen to meet the Don at his funeral parlor, turns to his wife and says, "I curse-a the day when you and Commore Corleone became friends." I hear it as "Commore" (Godmother), but it could have been Carmela.

In III, at Michael's party, Mary presents a check for $100 million to Archbishop Gilday from, I believe, "the Vito and Carmela Corleone Foundation."