Postgres 13

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CREATE TABLE leads (id int, user_details jsonb);

INSERT INTO leads VALUES (generate_series(1,10000),('{"name" : "'||random()::text||'", "country" : "IN", "phone_no" : "123456789"}')::jsonb);
INSERT INTO leads VALUES (42,'{"name" : "John Doe", "country" : "IN", "phone_no" : "123456789"}'::jsonb);
INSERT INTO leads VALUES (generate_series(1,10000),('{"name" : "'||random()::text||'", "country" : "IN", "phone_no" : "123456789"}')::jsonb);

CREATE TABLE

INSERT 0 10000

INSERT 0 1

INSERT 0 10000

EXPLAIN (ANALYSE,COSTS OFF)
SELECT * FROM leads
WHERE lower(user_details->>'name') ~~ '%doe%' 

QUERY PLAN

Seq Scan on leads (actual time=8.232..14.977 rows=1 loops=1)

  Filter: (lower((user_details ->> 'name'::text)) ~~ '%doe%'::text)

  Rows Removed by Filter: 20000

Planning Time: 0.465 ms

Execution Time: 15.289 ms

EXPLAIN

CREATE INDEX leads_user_details_name_idx ON leads 
USING gin( lower((user_details->>'name')) gin_trgm_ops);

CREATE INDEX

EXPLAIN (ANALYSE,COSTS OFF)
SELECT * FROM leads
WHERE lower(user_details->>'name') ~~ '%doe%' 

QUERY PLAN

Bitmap Heap Scan on leads (actual time=0.439..0.440 rows=1 loops=1)

  Recheck Cond: (lower((user_details ->> 'name'::text)) ~~ '%doe%'::text)

  Heap Blocks: exact=1

  ->  Bitmap Index Scan on leads_user_details_name_idx (actual time=0.418..0.418 rows=1 loops=1)

        Index Cond: (lower((user_details ->> 'name'::text)) ~~ '%doe%'::text)

Planning Time: 3.523 ms

Execution Time: 0.496 ms

EXPLAIN