Unfortunately, we do not have an option to allow the admin to set which data key option to show for the Joomla full name field from the advanced search section.

The reason is because the system can't determine that what name format user registered on the site, imagine if the admin configures to use "First name, Last name" at first while the user registered on the site using this name format, then the admin decides to change the name format to "single name" so with this field setting changes, it doesn't automatically change the existing user name format since the name-value already stored in the database.

So if the advanced search data key option respects the field name format, then the user might be not able to find the first batch of whoever registered on the user since those registered users enter the "First name, Last name" format during registration.