How to use LIKE with subquery?
I think this is what you are after, no need for Regex. It's just a correlated subquery, with the only difference being the LIKE condition instead of the common equality condition:

SELECT b.* 
FROM tablename AS b 
WHERE EXISTS 
      ( SELECT * 
        FROM words AS w 
        WHERE b.name LIKE '%' || w.word || '%'
      ) ;