MySQL CASE to update multiple columns

UPDATE tablename
SET col1 = CASE WHEN name="name1" THEN 5 
                WHEN name="name2" THEN 3 
                ELSE 0 
           END
 , col2 = CASE WHEN name="name1" THEN '' 
               WHEN name="name2" THEN 'whatever' 
               ELSE '' 
          END
;