Hi Jo,

Without dev

In the purchase order, when you type text on vendor reference, the text is in the display name of the purchase order, for example P00014 (THIS A VENDOR REFERENCE). 

The vendor reference is usually used to type the vendor's invoice's number or RFQ's reference.

With dev

If this does not answer your needs, you can do it with only Python. 

1) Create a custom module
2) In  your module ,  add the field doc_name in purchase.order model.
3) Implement/override display_name for model purchase.order to return doc_name.

Once this is done, Odoo will always display doc_name.

I just updated this answer with the code

Python : models.py

class PurchaseOrder(models.Model):
    _inherit ='purchase.order'

    custom_name = fields.Char()
    @api.depends('custom_name')
    def _compute_display_name(self):
        for this in self:
            this.display_name = this.custom_name

This works for all model.