SELECT wc1.id AS category_id, wc1.name AS category_name,
        if(wc3.parent_id is not null, wc4.name,
           if(wc2.parent_id is not null, wc3.name,
              if(wc1.parent_id is not null, wc2.name, wc1.name))) as ultimate_parent
    FROM CATEGORIES wc1
    LEFT JOIN categories wc2 ON wc1.parent_id = wc2.id
    LEFT JOIN categories wc3 ON wc2.parent_id = wc3.id
    LEFT JOIN categories wc4 ON wc3.parent_id = wc4.id;

SELECT wc1.id AS category_id, wc1.name AS category_name,
        if wc3.parent_id is not null then wc4.name,
           if wc2.parent_id is not null then wc3.name,
              else wc1.parent_id is not null Then wc2.name, wc1.name as ultimate_parent -- I am having issues with splitting the last if clause
    FROM CATEGORIES wc1
    LEFT JOIN categories wc2 ON wc1.parent_id = wc2.id
    LEFT JOIN categories wc3 ON wc2.parent_id = wc3.id
    LEFT JOIN categories wc4 ON wc3.parent_id = wc4.id;

SELECT wc1.id AS category_id, wc1.name AS category_name,
       (case when wc3.parent_id is not null then wc4.name
             when wc2.parent_id is not null then wc3.name
             when wc1.parent_id is not null then wc2.name
             else wc1.name
        end) as ultimate_parent
FROM CATEGORIES wc1 LEFT JOIN
     categories wc2 ON wc1.parent_id = wc2.id LEFT JOIN
     categories wc3 ON wc2.parent_id = wc3.id LEFT JOIN
     categories wc4 ON wc3.parent_id = wc4.id;