Thank you very much, but unfortunately that does not achieve the goal.

No third party apps used because its odoo online version 16.2

By default, the context is TRUE, but when positioning to search in the field, only the customer's name is shown and not the VAT.
Only after selecting the client does the VAT number appear under the client's name, and what will make life easier for millions of Odoo users is that when searching, the VAT number appears, just when you write the first letters of the customer name and next to the name the VAT number is displayed before pressing the enter key or clicking.
Any suggestions to achieve this?
Thank you!

Hi,

If you need to show vat number along with the partner name in any many2one field of res.partner, you just need to pass show_vat as True in the context.

Sample:

context="{'res_partner_search_mode': 'customer', 'show_address': 1, 'show_vat': True}"

Thanks