The first box is First Names so you include the middle name here. The second box is Last Names which is where the maiden name goes. There is not a box for the married name but you could put it in the Other Information as an alternate name. So Sandra Dee Smith who married Harry Jones is First Names Sandra Dee and Last Names Smith.
If you go to the person whom you want to add/change their name, you go into their profile, click the edit button by their name and you should be able to add the middle name as well as change your mother's maiden name.
As for her married vs maiden name, it is recommended you use the maiden name.
You can list her married name as an alternate name. For women married more than once it is easier to track the maiden names and marriages. Shannon gave you a very good answer and this is just an additional thought.
womens names should always be entered as the Maiden name as the primary name.
where did you see "married name"??
@Rita Kay Cox
Here are some "Knowledge Articles" in 'FamilySearch':
How do I change vital information in Family Tree?
How should I enter names in Family Tree?
Where it states
Enter the person’s family name or surname.
If a woman changed her surname after marriage, enter her maiden name.
I hope these help.