With this new and powerful tool one can create multiple copies of the same file, each one watermarked with the text of your choice from a list.

IMPORTANT: If you don't have Acrobat, or are interested in a more powerful version, suitable for processing large amounts of files), there's also a standalone version of this tool available here.

UPDATE: Now available, a free DEMO version of this tool. This version will process up to 3 items in your list, adding the watermark text to the top-left corner of the first page of the document, with a fixed font style and size.

For example, let's say you want to distribute a movie script to multiple people, and want to stamp each copy with the name of the recipient, to prevent the script from being leaked. You create a list of all the people in the production team, like so:

You then open your script and run the tool from the Tools menu.
You select your list and set the properties of the watermark text:

As you can see, you can set various options regarding the location and style of the text, as well as which pages to watermark and under which name to save the watermarked files.
The tool will proceed to create watermarked copies of the file, one for each item in the input file.

The result:

The folder with the watermarked files (notice the file names):

One of the watermarked files:

Later on, the files can be secured using a batch process to ensure that the watermarked texts can not be edited.

Note: This is not actually a batch process, so you don't have to have Acrobat Pro to use this tool. Any version of Acrobat will do.

You can download the sample PDF files and Names list shown above from here.