If you want to do role-based invoicing in CORE so that the employee titles appear on invoices instead of employee names, you first need to make sure that you have added titles for the employees on the Employees > General > Details screen. After creating invoices from the time entries of the employees, you need to choose the proper invoice template that displays the titles of employees (For example, Hourly Invoice by Title). Check CORE Help Center for details on choosing invoice templates.
By default, the title of an employee is copied to the Classification field of the time entries of the employee and this field is what shows up as the title on the corresponding invoices. If you want to be more flexible and have different titles for the same employee on different projects or different roles on the same project, you can skip adding the title at the employee level and instead add a classification at the fee schedule level. It takes priority over the employee title and the time entries inherit the classification from the fee schedules. Check CORE Help Center for details on Classification in Fee Schedules.