Greetings!
This is a great question! As such, I took the past few days researching it and the answer I have to your question is: "kind·a"
As you said, inserting a FIELD will result in the full filepath and I have not been able to 'format' this field to report just the filename.
However, Page Setup handles these fields differently! As such, referencing
&[FILENAME] as an entry into the Header/Footer will print the filename without the filepath.
Please note, that the Page Setup Header/Footer inputs will only populate if the Header/Footer regions of your Worksheet are left blank.

Hope this of help!
- Kenny Lemens, P.E. ᵂᴵ
"No matter where you go, there you are." -Buckaroo BanzaiHotkeys: https://en.smath.com/forum/resource.ashx?a=45771&b=2