Yes, this is possible. You can override the name_get method per field using a related field combined with a custom widget, but the cleanest approach is to use a computed field that returns the value you want to display.

For your second field, instead of a Many2one, use a related field pointing directly to client_order_ref:

python

sale_order_ref_id = fields.Many2one('sale.order')
sale_order_client_ref = fields.Char(
    related='sale_order_ref_id.client_order_ref',
    string='Customer Reference',
    store=False
)

Then in your view, show sale_order_client_ref instead of sale_order_ref_id for the second field.

If you need it to remain a Many2one for filtering/domain purposes, another option is to create a custom widget in JS that overrides how the field value is displayed — but that's significantly more complex and rarely necessary for this use case.

The related field approach is the Odoo standard way and works cleanly in v13.