Problem with adding name and lastname on registration

Hi there,
I’m using classipress theme and I addedd some extra field-s on user registration like name and lastname. My problem is that somethimes, name and last name are inserted into database, and somethimes not. I don’t get it what I’m doing wrong.

On the template page it look’s like this:

<label for="first_name"><?php _e('Ime:', 'APP_TD'); ?></label>
<input tabindex="2" class="text" type="text" class="text required" name="first_name" id="first_name" value=<?php if (isset($_POST['first_name'])) echo esc_attr(stripslashes($_POST['first_name'])); ?>>

<label for="last_name"><?php _e('Prezime:', 'APP_TD'); ?></label>
<input tabindex="3" class="text" type="text" class="text required" name="last_name" id="last_name" value=<?php if (isset($_POST['last_name'])) echo esc_attr(stripslashes($_POST['last_name'])); ?>>

and in the function file of the theme I added this:

function at_validate_custom_fields( $login, $email, $errors ) {

  // fields to be validated
  $fields = array(
	'first_name' => __( 'Ime:', 'APP_TD' ),
	'last_name' => __( 'Prezime:', 'APP_TD' ),
  );

  // check for empty required fields an display notice
  foreach ( $fields as $field => $value ) {
	if ( empty( $_POST['first_name'] ) ) {
		$errors->add('empty_fields', __('<strong>GREŠKA</strong>: Niste uneli ime.', 'APP_TD'));
	}
	if ( empty( $_POST['last_name'] ) ) {
		$errors->add('empty_fields', __('<strong>GREŠKA</strong>: Niste uneli prezime.', 'APP_TD'));
	}
  }

  // check for invalid names (letters and spaces)
  if ( ! empty( $_POST['first_name'] ) && !preg_match("/^[\p{L} ]+$/u", $_POST['first_name']) ) {
	$errors->add('invalid_name', __('<strong>GREŠKA</strong>: “', 'APP_TD').$fields['first_name'].__('” u polje za ime trebate upisati samo slova.', 'APP_TD'));
  }
  if ( ! empty( $_POST['last_name'] ) && !preg_match("/^[\p{L} ]+$/u", $_POST['last_name']) ) {
	$errors->add('invalid_name', __('<strong>GREŠKA</strong>: “', 'APP_TD').$fields['last_name'].__('” u polje za prezime trebate upisati samo slova.', 'APP_TD'));
  }  

// additional custom fields validations here

}
// validate custom fields
add_action( 'register_post', 'at_validate_custom_fields', 10, 3 );

// register the extra fields as user metadata
function at_register_custom_fields( $user_id, $password = "", $meta = array() )  {

	// custom fields
	$fields = array(
		'first_name',
		'last_name',
	);
        // cleans and updates the custom fields
	foreach ( $fields as $field ) {
	    $value = stripslashes( trim( $_POST[$field] ) ) ;
	    if ( ! empty( $value ) ) {
	  	 update_user_meta( $user_id, $field, $value );
	    }
	}

}

// save the custom fields to the database as soon as the user is registered on the database
add_action( 'user_register', 'at_register_custom_fields' );

since I changeg defaulf displaying name like this:

add_action('user_register', 'registration_save_displayname', 1000);
function registration_save_displayname($user_id) {
    if ( isset( $_POST['first_name']) &&  isset( $_POST['last_name']) ){
		$pretty_name = $_POST['first_name'] . ' '. $_POST['last_name'];
		wp_update_user( array ('ID' => $user_id, 'display_name'=> $pretty_name) ) ;
	}
}

this is always saved in database, but name and lastname fields, not.