If you set a business process to be Public, then no one needs to login when fill in the form. So the initiator of the instances will show up as Anonymous. 

To add to this discussion from 2016... I just discovered that one of our forms that was built in April 2022 is naturally and properly filling in the original submitter with Anonymous User, however, what I didn't realize until today is that the Supervisors that get assigned to review the form are also getting their "Supervisor Reviewing" field ending up with Anonymous User EVEN THOUGH I programmed the field to fill in with the current user. 

This is because they are logging in off their cell phones, following the link from the email notifications, and not bothering to log into LF Forms.  This is not as intended, but no one spotted it until today.

So, the only things I can think of to get a proper name in there is to make the field Required and force them to type their own names in there... or get the field filled by copying the name that was added by the original submitter when they declared who their supervisor was.