Is automatically renaming indexes when renaming columns relevant for database health/maintenance?

I am currently building out a few features for a project where customers are able to change up their database schema via an UI and we handle all the nitty-gritty details on running the required statements to update the database (PostgreSQL). I did a bit of research on what some gotchas could be and one of the gotchas we've ran into are the index names, especially those that are auto-generated when creating UNIQUE constraints. We allow the users to declare which column they want indexed, but we didn't realize that we now create two indexes whenever they set indexed to true on a UNIQUE column. This is solved now already, however this raised the question on what happens when columns are renamed. As far as our testing goes, renaming columns does not change the index names and when then creating a new column with the previously occupied name an index with a number appended gets created:

CREATE TABLE users (
		user_id SERIAL PRIMARY KEY,
		email VARCHAR(255) UNIQUE NOT NULL
);

ALTER TABLE "users" RENAME COLUMN "email" TO "email_one";
ALTER TABLE "users" ADD COLUMN "email" INTEGER UNIQUE;

/*
postgres@localhost:postgres> \d users
+-----------+------------------------+----------------------------------------------------------+
| Column    | Type                   | Modifiers                                                |
|-----------+------------------------+----------------------------------------------------------|
| user_id   | integer                |  not null default nextval('users_user_id_seq'::regclass) |
| email_one | character varying(255) |  not null                                                |
| email     | integer                |                                                          |
+-----------+------------------------+----------------------------------------------------------+
Indexes:
    "users_pkey" PRIMARY KEY, btree (user_id)
    "users_email_key" UNIQUE CONSTRAINT, btree (email_one)
    "users_email_key1" UNIQUE CONSTRAINT, btree (email)
*/

Since I am not a database expert and haven't maintained large databases at all I am unsure if this could possibly ever lead to issues. I asked a friend of mine and he gave me the following function that I could use instead of RENAME TO:

CREATE OR REPLACE FUNCTION rename_column_and_index(
    tbl_name TEXT,
    old_col_name TEXT,
    new_col_name TEXT
) RETURNS void AS $$
DECLARE
    index_record RECORD;
    old_index_suffix TEXT;
    new_index_name TEXT;
BEGIN
    -- Find all indexes that contain the old column name
    FOR index_record IN
        SELECT indexname
        FROM pg_indexes
        WHERE tablename = tbl_name
          AND indexdef LIKE old_col_name || '%'
    LOOP
        -- Start a savepoint
        EXECUTE 'SAVEPOINT before_rename';

        BEGIN
            -- Extract the suffix from the old index name
            old_index_suffix := substring(index_record.indexname from length(quote_ident(old_col_name)) + 1);
            -- Create the new index name
            new_index_name := quote_ident(new_col_name) || old_index_suffix;

            -- Rename the column
            EXECUTE 'ALTER TABLE ' || quote_ident(tbl_name) || 
                    ' RENAME COLUMN ' || quote_ident(old_col_name) || 
                    ' TO ' || quote_ident(new_col_name);

            -- Rename the index
            EXECUTE 'ALTER INDEX ' || quote_ident(index_record.indexname) || 
                    ' RENAME TO ' || new_index_name;
        EXCEPTION
            WHEN OTHERS THEN
                -- Rollback to the savepoint in case of error
                EXECUTE 'ROLLBACK TO SAVEPOINT before_rename';
                RAISE;
        END;

        -- Release the savepoint
        EXECUTE 'RELEASE SAVEPOINT before_rename';
    END LOOP;
END;
$$ LANGUAGE plpgsql;

-- SELECT rename_column_and_btree_index('users', 'email', 'email_one');

Now my question is: Am I too fearful of this issue? Is this function any good / makes future maintenance easier? Or can I just stop worrying about the automatic indexes completely?