There is not an easy answer to your question as the topic of a woman's name maiden or married is not always obvious. And, it can be variable depending on culture and local and family custom.
In most of the areas of the US that were settled by UK immigrants, the wifes maiden name may be on the stone, as in your example, but she was known by her husband's surname at time of death. Alas, you can not assume that a "surname" in the second position is a maiden family name. It might also be a familial surname but given to her as a second or middle name at her birth. An example would be a woman whose mother or grandmother's maiden name was Stewart, and she was given the name of Mary Stewart Powers at birth. She later married a Mr. Martin. Her stone might read Mary Stewart, wife of James Martin, or it might read Mary S Powers, wife of James Martin. You would not be able to know which of those was her maiden name.
However, if you can do a little research (as in Ancestry) very often you can find another sources that will tell you if that is a familial honor name, a maiden name, or a previous marriage name.
All that being said, some users will transcribe what you have described as Doe in her maiden name field, and Smith in the Family name field, with the understanding that the search engines will find here regardless of where the Doe is placed.
I also think we need to be more careful with recent and very modern graves, as there are now examples of same-*** couples and those in which the wife keeps her maiden name as her also legal name. .
I really wish BG would give us several surname fields, as in Maiden, 1st Marriage, 2nd Marriage, 3rd Marriage,
Hope this helps. If you have to "interpret" try to educate yourself on the local name customs as best you can.