It's usually a field with a calculation. Go into Manage Database, select the fields tab, and the correct table. Scroll down the fields and look for a field called "Contact Name Labels", or "Contact Name". You're looking for a field that combines Last Name & First Name and/or Company Name as a calculation.
Also if you put the layout in Layout mode, you should see the label and what Table::Field it references.
Copy/Paste will only work if all Tables/fields referenced in the 'copy' side, match Tables/fields in the 'paste' side.
The starter solutions that come with FileMaker 11 and 12 are not the same. Which version do you have? On what layout are you on when you see this label?