SOLVED!
Thanks BastianHammer, that video was helpful. To simplify it for others, here are the exact steps I did to make account names searchable in Targets:
Copy the core Prospects SearchFields.php file to the custom directory so it’s not overwritten by updates:
sudo cp /var/www/html/crm/public/legacy/modules/Prospects/metadata/SearchFields.php /var/www/html/crm/public/legacy/custom/modules/Prospects/metadata/
Edit the file and add this block directly following
$searchFields[‘Prospects’] =
array(
INSERT THIS:
‘account_name’ => array(
‘query_type’ => ‘default’,
‘db_field’ => array(‘account_name’),
‘force_unifiedsearch’ => true
),
THE REST OF THE FILE IS BELOW THIS SECTION
Save the file and exit the editor
Admin → Repair → Quick Repair and Rebuild