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If I'm correct, you know how to create dynamic stamps? If not read here: https://helpx.adobe.com/acrobat/kb/create-custom-dynamicstamp.html
From inside a stamp script the "this.documentFileName" will return the name of the stamp file, not the name of the file being stamped.
Use this code in a calculation script on the stamp to put the name of the file being stamped into the field.
event.value = event.source.source.documentFileName;
This is code is undocumented. You can read all about it here:
Find out everything you ever wanted to know about stamps here: