Watermarking same PDF for multiple unique recpients

Is this watermark just the persons name? Where does it need to appear on the page? Is it on all pages?

You can write a simple script to do this from the Console window.

You'll find a tutorial here on the Console, infact you should watch several of these videos to get a grounding in Acrobat scripting:

https://www.pdfscripting.com/public/Free_Videos.cfm#JSIntro

Here's the reference entry for the watermark function:

https://help.adobe.com/en_US/acrobat/acrobat_dc_sdk/2015/HTMLHelp/#t=Acro12_MasterBook%2FJS_API_AcroJS%2FDoc_methods.htm%23TOC_addWatermarkFromTextbc-10&rhtocid=_6_1_8_23_1_9

try it by running it in the Console window:

this.addWatermarkFromText({cText:"My Name"});

Writing the full script is a bit of work.  Contact me through www.windjack.com if you are interested in hiring a developer.