In that case your subject line is misleading. There's nothing built in to
maintain a list. You could provide that functionality by writing macros
named FileSave and FileSaveAs to intercept those commands, and to add the
current user's name to a list maintained in a custom document property or a
document variable just before doing the actual save.
Before you go to that much trouble, though, ask yourself the purpose of
this. Is it sufficient to know the list of names, or do you also want the
date/time and perhaps to be able to identify what changes were made in that
session? If so, you really want a document control system, not a home-grown
macro solution. There are many such programs, including at least one free
one. Check Google for "document control" and "version control".