Not the best way to handle.

First, "an old document." You don't want to change a name in an old document
but in a new document. Your old document should probably be a template if
you are using it this way.

Second, you can set up a separate template that holds AutoText entries
including this name. This is saved as a global template. See
http://addbalance.com/word/movetotemplate.htm for step-by-step instructions
on moving / sharing / copying / backing-up customizations including
AutoText, AutoCorrect, keyboard assignments, toolbars, macros, etc.

I would set my document template up with an AutoText field that reflects
this AutoText entry. Then have an AutoNew macro in the template that unlinks
the AutoText field when an new document is created. This way your templates
will be up to date while your new documents will have the correct
information.