Fetch data from a WP page with same name as current username

According with docs, when you want to retrieve field attached to post using get_field / the_field you should pass a numeric ID as 2nd argument.

You are passing a string.

So your code should work if:

$login = wp_get_current_user()->user_login;
$page = $login ? get_page_by_path( $login ) : false;
$field = $page ? get_field('my_custom_field', $page->ID) : false;