If you don't want to give permission VIEW for staff member to be able to see all customers, you can assign staff member as admin to specific customer/s.
Go to the customer profile from the admin area and click on the Customer Admins tab.
Click on the assign admin button and choose the member/s you want to be assigned as admins to this specific customer.
Save the changes.
The member/s you assigned will now be able to see this customer along with the Customer menu item without having the permission for customers VIEW.