If you do not want to show employees on invoices, you can do that by editing the relevant invoice template in Global Settings > Invoice Templates. Click Detail for the invoice template and in the Edit Template screen, under Layout, select the option Summarized for Time Details and Expense Details. Save the changes and Core prompts you to save it as a new template. Check Core Help Center for details on editing invoice templates.
Now change the invoice template to the new one here in Global Settings under Template Assignments. The invoices now display only summarized time and expenses without the employee names.