It would help if you mentioned the PDF program you're using.
From what I've seen on Adobe, you have to flatten the pdf first add the watermark then save, but beware, I believe it turns it into an image and kills any functionality of the input fields, meaning if anyone wants to use the form they have to print it out first and fill it in manually, but their all different in how they go about creating the watermark, that's why I asked what program you're using.
I did find
How to Create and Apply a Watermark to PDF Documents | Chron.com There is the free version of PDF Watermark Creator (link in Resources) that might work.
Didn't the suggestions earlier this year from
add unremovable watermark to a pdf work out?