Thank you for your prompt reply.
In the I scan for a date within the document and set a custom meta date field. (This still cannot be done, without using a script, correct?). Then I change a custom meta field to the value “ready to be renamed”:
In the following rule I check, if the custom meta field is set to “ready to be renamed” and change the file name using the date which is set in the the custom meta date field which was set in the rule before: