When you place a section and look at the type parameters you will see that the section head is another family
When you edit that section head family you will notice it uses several labels. You can add additional labels. However in this case it is limited to the parameters given. As you can see it is not possible to add your own (shared) parameters.
So you are limited to the parameters given
Louis
Please mention Revit version, especially when uploading Revit files.
As Louis said open the section head family then you have to make a new or copy an existing label edit this label see pics below
You can create completely your company standard section head with the labels you like.
save as your section head family and load it into your project.
Parameter "View Name" is editable as you wish.