Question about custom code

I am using the following code to combine First name, Last name, and Username to set it as a display name.

add_action( 'profile_update', 'my_profile_update', 10, 2 );
function my_profile_update( $user_id, $old_user_data ) {
        // Do something
	$user = get_user_by( 'id', $user_id );
	$firstname = $user->first_name;
	$lastname = $user->last_name;
	$username = $user->user_login;
	if (  $firstname !== '' && $lastname !== '' ) {
	    remove_action( 'profile_update', 'my_profile_update', 10, 2 );
	    wp_update_user( array( 'ID' => $user_id, 'display_name' => $firstname.' '.$lastname.' '.$username ) );
	}
}

Typically this works fine as profile gets updated.

Then I realized the above code doesn’t work when when our customers are creating an account at the checkout page going through paypal.

The payment process goes like this:

checkout page -> click Paypal -> Page redirects to Paypal -> customers make a payment at paypal.com -> payment processed and click “go back to the merchant page” -> back to our website with “Thank you, your order is received” page

And I think while the checkout process goes through many steps with paypal, somehow the above code doesn’t work. Display name is not altered.

I am trying to see if there is anyway the display name could be set to first+last+username even they go through paypal process?