If you are using MTO, you can get the customer from the sales order.

Enable Developer Mode.

Create a many2one field on the Manufacturing Order (production.order) linked to Contacts (res.partner).

Here's how to do it in Studio: 

Now we can add some Python code to get the customer from the sales order (if you are using MTO).

First I renamed the field to x_studio_customer but that is optional.

Then click on MORE in the left-hand panel.

After you click on MORE you will see the field details:

for record in self:
  if record.origin:
      if record.sale_order_count:
          order = record.env['sale.order'].search([('name','=',record.origin)])
          if order:
            record['x_studio_customer'] = order.partner_id

[Extra lines of code added]

Once completed, this shows the customer from the sales order (for MTO):

NOTE:

This works when a Manufacturing Order is created on confirmation of a sales order.  It won't set the customer for existing sales orders.

For that, there are two options:

1. Use a server action, as per this answer
2. Set the new field not to be stored.  I have had problems with this in the past, but it can be worth trying.

I think you could use the same logic to get the project name.

The search method may return nothing if the origin field is not populated. He may need to ensure he is running MTO, so the origin field gets populated.

thanks I follow the steps but I cannot change the field name, give me this error:

Missing Record

Record does not exist or has been deleted. (Record: ir.ui.view(6066,), User: 2) and when I change it to the code nothing happens.