WordPress Plugin:Search for name, slug or description in the tag search in /wp-admin/edit-tags.php?taxonomy=post_tag.

extended-admin-tag-search.php

<?php
/**
 * Plugin Name:  Extend the tag search 
 * Description:  Search for name, slug or description in the tag search in /wp-admin/edit-tags.php?taxonomy=post_tag.
 * Plugin URI:   https://gist.github.com/birgire/4a43dbe1b7566aa0f162b59066276d15
 * Author:       birgire
 * Version:      1.0.0
 */
 
 /**
 * Target the correct get_terms() instance on edit-tags.php and replace the search with the
 * custom _name_or_slug_or_description__like attribute
 */
 
add_filter( 'get_terms_args', function( $args, $taxonomies )
{	
    if(    
        did_action( 'load-edit-tags.php' )						// Target the edit-tags.php  
	    && 'post_tag' === filter_input( INPUT_GET, 'taxonomy' ) // Target post tags
	    && isset( $args['search'] ) 							// Target the search mode	
		&& 'all' === $args['fields']							// Exclude the get_terms() instance with term count
		&& ! isset( $args['largest'] )  						// Exclude the get_terms() instance within wp_tag_cloud() 
	  ) {
		    $args['_name_or_slug_or_description__like'] = $args['search'];
    		unset( $args['search'] ); 
    } 
	
   	return $args;	
   	
}, 10, 2 );

/**
 * Support the custom _name_or_slug_or_description__like attribute of get_terms()
 */
add_filter( 'terms_clauses', function( $clauses, $taxonomies, $args ) use ( &$wpdb )
{
    if(    
           ! empty( $args['_name_or_slug_or_description__like'] ) 
		    && ! empty( $clauses['where'] ) 
   	) {
	
		$like = '%' . $wpdb->esc_like( $args['_name_or_slug_or_description__like'] ) . '%';
		
	    $clauses['where'] .=  $wpdb->prepare( 
		    " AND ( t.name LIKE %s OR t.slug LIKE %s OR tt.description LIKE %s ) ", 
		    $like,
		    $like,
		    $like
		);
	}
	  
    return $clauses;
    
}, 10, 3 );