Duke
The wife of a duke is a Duchess. This is an honorary title, given for life to the lawfully wedded wife of a Duke. If she divorces and remarries a commoner, (person with no title) their children have no title. The children of a duke, on the other hand, do have honorary titles (so long as they are born in lawful wedlock). The eldest son may bear what is called a junior title which an ancestor was given before the dukedom was created. Other children would be called 'Lady' Jane (or other Christian name) and 'Lord' James (or other Christian name). Children use the family surname, not the Dukedom.