I usually do this for shorter strings:

CREATE EXTENSION btree_gist;
CREATE EXTENSION pg_trgm;

CREATE INDEX "idx1"
  ON data
  USING gist
  (((name::text) COLLATE pg_catalog."default" gist_trgm_ops);

Now, construct the query like so in 9.1+:

SELECT name FROM data WHERE name LIKE '%Jack%';

This will make an index-only scan and that’s not all! Works very well with UTF-8 too.

The trigram documentation has a bit more search options (regex in 9.3+).