In the UK if Dame Jane Doe marries Sir John Smith does she remain Dame Jane Doe, become Dame Jane Smith, or become Lady Smith? Does it matter what kind of she has a higher ranking damehood than his knighthood? Is there even a set rule?
Traditionally titles held in own right were to be used in preference to ones which came as a courtesy, so she would be Dame Joe Doe/Smith depending if she wished to change her name.
She could also use Lady Smith DBE, the post nominals depending on exactly which order she was a member of (in the above example its Dame of British Empire)
If *both titles *are courtesy ones then she would use the highest ranking one, sometimes combining them. To take an example, the Queen’s cousin,Princess Alexandra the Queen’s cousin is a Princess by virtue of being Grandchild of a monarch in the male line. She remained Princess Alexandra even after she married Angus Oglivy. When he was knighted she remained Princess Alexandra, but could in her full title add be called Princess Alexandra, Lady Ogilvy.
The Queen herself was known as Princess Elizabeth even after her marriage, the full title being “Princess Elizabeth, the Dutchess of Edinburgh”.
Examples where this has been an issue are rare but not completely unknown. One would be Mary Donaldson, who, as the wife of (the then) Sir John Donaldson, was Lady Donaldson until 1983, when, on becoming a DBE as Lord Mayor of London, she became Dame Mary Donaldson.
There is also the issue that ‘Dame’ can actually be used as the style for the wife of a knight, but while that is hypercorrect, it is also extremely archaic.