Select one single row from table b for each row from table a
How about this:

Select * 
from 
  tableB b
 inner join
  (select a.*, row_number() over (partition by a.type order by a.type) rn from tableA a) a1
    on b.type=a1.type and a1.name='SEARCHED_NAME' and a1.rn=1


PS. Not tested, as you didn't provide a script to create and populate the tables.