Hi,

If you need to achieve this without any customization, you can record the nick name in the field Reference.  If you open contacts form, under the Sales & Purchase page, under the Misc section, you can see the field named Reference, here you can record the extra name of the customer. Using this reference, you can search and find the partner in sales, purchase etc.

If you don't need the above, you can inherit the res.partner model and add a new field and add it to the name search function.

Thanks