There are probably a number of ways. The more sophisticated would involve a macros.

The only semi-simple way I can think of to do this would require that you know, in advance, the user name the person will use for logging in to Word. This may or may not be the same name they use in Windows.

Then you could store your alternatives as AutoText (one of the quick parts) in your document's template and use IF fields to test for the user name and display the appropriate AutoText entries using AutoText fields. (Actually, you could have the entire text inside the IF field rather than an AutoText field, but that would really bloat your documents.)

In part, it depends on how sensitive the text you are hiding is. There is nothing secure about this solution.

Again, AutoText must be stored in a template. Your users would be creating new documents based on the template, not opening the template.

You could have an AutoNew macro in your template that would update and unlink all the AutoText fields and then all the IF fields. It could even, after doing that, attach the document to the user's normal template breaking access to your non-displayed AutoText.

So, the answer is, yes, it can be done. It depends on how much effort you want to put into it.

Automated Boilerplate Using Microsoft Word
AutoText field
IF field