There are two formats for Arabic names.
In one format, there is the given (first) name, followed by the father's first name, followed by his father's first name. This is used for males and females alike. The alternative format is to have the given (first) name, followed by the father's first name, followed by the family name. Classical names go back further, listing patrilineal first names, and include a النَّسبة nisba adjective for the city of birth and also a nickname/adjective describing an attribute of that person.
Arab women do not take their husband's name when they marry. However, in some regions the women are addressed by their husband's family name.
In Arabic, refer to someone by their first name preceded by a title.
In introductions and formal settings, also include the person's father's first name.
أنا أسمي محمد
My name is Mohammed.
miss (unmarried woman)