Renaming an ENUM value in Postgres 9.5

enum.sql

-- assuming your existing type is as follows
CREATE TYPE user_types AS ENUM
( 'user',
  'admin',
  'foo'
);

-- here's how you rename the 'foo' value to 'bar'
BEGIN;

    ALTER TABLE users ALTER COLUMN user_type SET DATA TYPE TEXT;

    -- if the column has a default value
    ALTER TABLE users ALTER COLUMN user_type SET DEFAULT 'user';

    DROP TYPE user_types;

    UPDATE users SET user_type = 'bar' WHERE user_type = 'foo';

    CREATE TYPE user_types AS ENUM
    ( 'user',
      'admin',
      'bar'
    );

    -- once more, if the column has a default value change the default before changing the column
    -- type, else Postgres won't know how to convert the existing default value to the new type
    ALTER TABLE users ALTER COLUMN user_type SET DEFAULT 'user'::user_types;

    ALTER TABLE users ALTER COLUMN user_type SET DATA TYPE user_types USING user_type::user_types;

COMMIT;