Wp cron event is set but the function isn’t getting fired

I’m a WP cron beginner trying to make some test function.

So i have a test page with this code:

if ( ! wp_next_scheduled( 'do_this_in_an_hour' ) ) {
wp_schedule_single_event( time() + 40, 'do_this_in_an_hour' );
}

And for the testing:

echo wp_next_scheduled( 'do_this_in_an_hour' );

echo '<pre>';
$cron_jobs = get_option( 'cron' );
var_dump($cron_jobs);
echo '</pre>';

And in my functions.php (not sure i have to put that there):

function do_this_in_an_hour() {
    wp_mail('mymail@gmail.com','this is a cron test!','great here is the massage!');
}
add_action( 'my_new_event', 'do_this_in_an_hour', 10, 3 );

Now i see that the cron job is added to the cron job array and i do get a timestemp for next_scheduled function and it is removed from the cron jobs array after i refresh when the time is passed (40 seconds), but the mail isn’t sending (of course in the real code i have my real mail address and i did test the mail function alone and it’s working).

Any idea what i’m doing wrong?

I needed the hook name and not the function name so instead of this:

if ( ! wp_next_scheduled( 'do_this_in_an_hour' ) ) {
wp_schedule_single_event( time() + 40, 'do_this_in_an_hour' );
}

That:

if ( ! wp_next_scheduled( 'my_new_event' ) ) {
wp_schedule_single_event( time() + 40, 'my_new_event' );
}