Here's the relationship tables:
Full name exists in all three tables where it should only be defined in Employees. Are you sure that Labor Allocation Reporting::FullName actually stores a name that matches to the FullName in employee? If not, $Employee Name will be blank.
ID use this relationship:
Labor Allocation Reporting::EmployeeID = Employees::EmployeeID
and delete the full name field from both Labor Allocation Reporting and Labor Allocation tables.
When you need the employee name on layouts based on those tables, you can include the Employees::FullName field on those layouts.
Your script could then use this set field step to specify a name:
Set Field [Employees::Fullname ; $Employee Name ]
If that does not resolve the problems you are having, please post back and tell us what results you do get when you run your script. (That it doesn't work doesn't help us to help you as much as knowing HOW it failed...)