Actually I recognised that his is not even necessary. If the file is exported as text file in FineReader the actual first date in the scanned letter is also the first date in the text (which is not the case in PDF due to inconsistent orders of different areas).
How can I rename the PDF version of the scanned letter using the first date found in the txt version?
Hazel for example can be told to identify the first date whereas DEVONthink is able to identify oldest, newest and document date (no idea of the process which also is not perfect).
With this rule you can use of the identified date to rename the pdf:
To stay on topic and once more refer to the script of @Silverstone, is it possible to make the script export a pdf and a txt?
For now I do this with an Automator folder action.