Using GROUP CONCAT in my-sql query with wp_usermeta table

How about a Pivot Query?

This would return rows that have first_name,last_name,user_login. You could then add whatever condition you wanted using a WHERE clause.

            SELECT

                    MAX(CASE WHEN wp_usermeta.meta_key = 'first_name' then wp_usermeta.meta_value ELSE NULL END) as first_name,
                    MAX(CASE WHEN wp_usermeta.meta_key = 'last_name' then wp_usermeta.meta_value ELSE NULL END) as last_name,
                    wp_users.user_login

                    FROM wp_users

                    LEFT JOIN wp_usermeta
                    ON wp_users.ID = wp_usermeta.user_id

                    GROUP BY wp_users.user_login