We are using in our company a couple of Brother-printers that have the ability to setup Restricted functions, so we deployed it so that the users need to enter a PIN before printing. In the printer, ...
Universal Print uses user information from Azure AD.
It may be worthwhile to reach out to Brother to ask them if their restricted functions can use the user's UPN or can parse the UPN to just use the 1st half of the value.
Alternatively, you mentioned that the printer is using the user name. If you change the user's display name within Azure AD to "j.doe", would that work? In the Azure AD portal, the field is called "Name". It is separate from the "First name" and "Last name" field. If you use Graph Explorer (Graph Explorer - Microsoft Graph), can you retrieve the user's profile, the field name in the result is "displayName".