How to add hundreds of uniquely named checkboxes to a PDF

That depends on what exactly is the workflow that you're trying to achieve.

For example, you can create a radio button with the name Group1 and make them look and behave like a checkbox.

Group1 is the name of the parent field for all of the copies (or children fields) that you need to make.

The cool thing about Radio Buttons is that when you crete a copy from Group1 (a children field) it will have its own export value (different from each other) and in the order that these radio buttons were created.

This is convenient as it  allows to have a mutually exclusive relationship; meaning that when you check  a different radio button, the radio button that was checked will uncheck and only the one that you're clicking on will become checked. If this is not what you're looking for then you will surely have to employ checkboxes.

The problem with checkboxes is that, even though it is possible to make a checkbox behave in the same manner as a radio button group(mutually exclusive),  it is not featured in Acrobat to have the ability to create multiple copies of the field with the same name (a prefixed parent field) for each checkbox, and produce a unique export value for each individual copy.  You'll be limited to  use "Create Multiple Copies" and manually create each group on the page that you want them.

You will need to develop your own script to handle that or get a paid for plug-in.    I believe that Adobe MVP try67 has developed a tool that just handle this.

You can check it out here: https://try67.blogspot.com/2010/10/acrobat-convert-duplicated-fields-to.html