A friend asked me this question recently because she wanted old schoolfriends to be able to contact her and also for old schoolfriends to recognise her when she tried to add them as friends.
I realised that I didn't actually know the answer beyond calling yourself Joe Blogs was Smith as your main name... but that I had seen the grey bracketed names as a suffix.
Between us, my daughter and I managed to work it out.
Alternative Name or Maiden Name in Brackets on Facebook
Click on the drop down menu at the top right of your blue tool bar.
Select the option for Settings.
This will bring you to your General Account settings
Edit the top option - Name
About half way down you will see the option to add an Alternative Name - add whatever it is that you want to put in here.
Then select to allow it to show on your Timeline.
If you don't allow it on your Timeline, then your profile will show up when people are looking for others with your maiden name but it won't show up in the grey brackets, so they might not make the connection between your married name and your old maiden name.
When you refresh, your Name at the top of your personal profile will show your current name and your maiden name in brackets in a lighter grey print beside it.
Privacy Settings After Showing Alternative or Maiden Name in Brackets on Facebook
My friend said that she did want people who were not friends of her existing friends to be able to contact her as her old school friends might not actually be part of her current set, so she changed the settings for 'People Who Can Contact Me' from Friends to Everyone so as to allow for this eventuality.