Postgres migration to new unique index

unique_index_migration.sql

/*
We have:
*/
CREATE TABLE data (id BIGINT, name VARCHAR);
CREATE UNIQUE INDEX ON data (name);
INSERT INTO data (id, name) VALUES (1, 'Alex'), (2, 'Bob'), (3, 'alex'), (4, 'AleX');

/*
If we put (3, 'Alex') then we get error:
*/
INSERT INTO data (id, name) VALUES (5, 'Alex');
--- ERROR:  duplicate key value violates unique constraint "data_name_idx"
--- DETAIL:  Key (name)=(Alex) already exists.

/*
But we decide that our unique constraint is not so strict and want to migrate and merge entries for new unique constaint
Just that is not working
*/
CREATE UNIQUE INDEX ON data ((lower(name)));
--- ERROR:  could not create unique index "data_lower_idx"
--- DETAIL:  Key (lower(name::text))=(alex) is duplicated.

/*
Decision is to move duplicates to temp table and then merge it
Duplicates we can select using Window Functions
*/
WITH duplicates AS (SELECT id, name, row_number() over (PARTITION BY lower(name) ORDER BY id ASC) FROM data)
SELECT * FROM duplicates WHERE row_number <> 1;
---  id | name | row_number 
--- ----+------+------------
---   3 | alex |          2
---   4 | AleX |          3
--- (2 rows)

/*
Copy it to special table
*/
CREATE TABLE duplicates (duplicate_id BIGINT, original_id BIGINT);
INSERT INTO duplicates (duplicate_id, original_id) (
  WITH marked AS (
    SELECT id, name,
      row_number() over (PARTITION BY lower(name)
                         ORDER BY id ASC) -- order is important, here
    FROM variation
  )
SELECT dupl.id, origin.id
FROM marked origin
LEFT JOIN marked dupl
ON lower(dupl.name) = lower(origin.name) -- our unique condition
AND dupl.row_number > 1
AND origin.row_number = 1
WHERE origin.row_number = 1 and dupl.row_number > 1);

...