Does divorce occur if the husband says "no" to his wife when she says "Madam so-and-so," intending to negate that name because she refused to say she was a servant?

Divorce occurs through explicit wording or through allusion accompanied by intention. So long as the husband did not intend to divorce his wife by denying her to be his wife, then no divorce takes place. The spouses must live together in kindness, and women are the sisters of men in rights, except for what the Sharia has specifically allocated. Guardianship (Qawamah) means looking after interests with mercy and benevolence, not domination and disregard for feelings. The degree of men over women is an encouragement to good companionship and to be generous towards them. A husband demanding his wife to declare herself a servant is a sign of bad companionship and character.