Obvious question. Do you have privileges to go into layout mode for that layout?
Perhaps it just looks like you can't enter layout mode?
Many address label layouts place data on the layout in a single text object consisting of multiple merge text fields. If you can get into layout mode, double click the text in order to edit it. To add a new field, press ctrl-M while your cursor is at the spot in the text where you want to see your field.
merge text will look like this: <<table::field>>
If you don't have merge text on your layout, ignore this post.
Try the following steps:
1 - In Layout mode double click inside the label to edit he field.
2 - Put the cursor at the end of Last Name field and press Enter key to create an empty line.
3 - Choose Menu - Insert - Merge Field
4 - Select Company Name.
The Labels layout acts like a text field where you insert merge fields.
I hope this works for you.