WordPress generate sequential numbered usernames when new users are created

functions.php

<?php

/**
 * Filters the errors encountered when a new user is being registered.
 *
 * The filtered WP_Error object may, for example, contain errors for an invalid
 * or existing username or email address. A WP_Error object should always returned,
 * but may or may not contain errors.
 *
 * If any errors are present in $errors, this will abort the user's registration.
 *
 * @since 2.1.0
 *
 * @param WP_Error $errors               A WP_Error object containing any errors encountered
 *                                       during registration.
 * @param string   $sanitized_user_login User's username after it has been sanitized.
 * @param string   $user_email           User's email.
 */
add_filter( 'registration_errors', 'smyles_allow_wp_login_register_empty_user_login', 9999, 3 );

/**
 * Allow empty user_login (username) from wp-login.php registration form
 *
 *
 * @since @@version
 *
 * @param $errors WP_Error
 * @param $sanitized_user_login
 * @param $user_email
 *
 * @return mixed
 */
function smyles_allow_wp_login_register_empty_user_login( $errors, $sanitized_user_login, $user_email ){

	// First remove empty_username error code to make sure there aren't any other errors
	$errors->remove( 'empty_username' );
	$error_codes = $errors->get_error_codes();

	// Return errors and don't process further (we only want to proceed when empty_username is only error code)
	if( ! empty( $error_codes ) ){
		return $errors;
	}

	return $errors;
}

/**
 * Generate sequential padded user_login
 *
 * @author Myles McNamara
 *
 * @return string
 */
function smyles_generate_next_seq_user_login(){

	// Use 0 as default (if option does not exist yet), as 1 will be used for first user
	$last_user_num = get_option( 'smyles_custom_seq_usernames_last_id', 0 );

	// Create padded username total length of 10 characters, increasing last ID by 1
	$gen_user_login = str_pad( (int) $last_user_num + 1, 10, 0, STR_PAD_LEFT );

	if( username_exists( $gen_user_login ) ){
		// If generated new user login exists, update our last id +1 and do recursive call
		update_option( 'smyles_custom_seq_usernames_last_id', (int) $last_user_num + 1 );
		return smyles_generate_next_seq_user_login();
	}

	return $gen_user_login;
}

add_filter( 'pre_user_login', 'smyles_custom_username_seq_pre_user_login' );

/**
 * Set user_login to generated value, only if passed value is empty
 *
 * @author Myles McNamara
 *
 * @param $sanitized_user_login
 *
 * @return string
 */
function smyles_custom_username_seq_pre_user_login( $sanitized_user_login ){

	$sanitized_user_login = trim( $sanitized_user_login ); // to match wp_insert_user handling

	/**
	 * The user_login should be empty string when creating from wp-login.php registration page,
	 * otherwise will contain a value when called by something else.
	 *
	 * There is a chance this will be called for updating a user (which is incorrect as wp_update_user should be called),
	 * but even when updating a user, the passed user_login should have some type of value.
	 */
	if( empty( $sanitized_user_login ) || $sanitized_user_login === 'GENERATE_CUSTOM_SEQ_USERNAME' ){
		$sanitized_user_login = smyles_generate_next_seq_user_login();
	}

	return $sanitized_user_login;
}

/**
 * Filters a user's meta values and keys immediately after the user is created or updated
 * and before any user meta is inserted or updated.
 *
 * Does not include contact methods. These are added using `wp_get_user_contact_methods( $user )`.
 *
 * @since 4.4.0
 *
 * @param array   $meta                 {
 *                                      Default meta values and keys for the user.
 *
 * @type string   $nickname             The user's nickname. Default is the user's username.
 * @type string   $first_name           The user's first name.
 * @type string   $last_name            The user's last name.
 * @type string   $description          The user's description.
 * @type bool     $rich_editing         Whether to enable the rich-editor for the user. False if not empty.
 * @type bool     $syntax_highlighting  Whether to enable the rich code editor for the user. False if not empty.
 * @type bool     $comment_shortcuts    Whether to enable keyboard shortcuts for the user. Default false.
 * @type string   $admin_color          The color scheme for a user's admin screen. Default 'fresh'.
 * @type int|bool $use_ssl              Whether to force SSL on the user's admin area. 0|false if SSL is
 *                                          not forced.
 * @type bool     $show_admin_bar_front Whether to show the admin bar on the front end for the user.
 *                                          Default true.
 * }
 *
 * @param WP_User $user                 User object.
 * @param bool    $update               Whether the user is being updated rather than created.
 */
add_filter( 'insert_user_meta', 'smyles_custom_username_seq_verify', 10, 3 );

/**
 * Verify user was created, and then increase option value
 *
 *
 * @author Myles McNamara
 *
 * @param $meta
 * @param $user WP_User
 * @param $update
 *
 * @return mixed
 */
function smyles_custom_username_seq_verify( $meta, $user, $update ){

	// Don't want to verify if this is just an update call
	if( ! $update && $user && $user->user_login ){

		// Check what the last user num was stored as
		$last_user_num = get_option( 'smyles_custom_seq_usernames_last_id', 0 );

		// Verify that user_login of the user that was created, matches what is supposed to be the next user_login
		if( (int) $last_user_num + 1 === (int) $user->user_login ){
			// Update our option after verification
			update_option( 'smyles_custom_seq_usernames_last_id', (int) $user->user_login ); // Type casting to int causes 0000000001 to be 1 (trim leading zeros)
		}

	}

	return $meta;
}

add_action( 'register_form', 'smyles_hide_wp_login_username_field' );

function smyles_hide_wp_login_username_field(){

	// Hide the first <p> element in registerform, which is the userlogin input
	echo '<style>#registerform p:first-of-type { display: none; }</style>';

}

This code allows you to create custom users from admin area specifying custom usernames, or use GENERATE_CUSTOM_SEQ_USERNAME to generate sequential numbered one. If using registration form other than wp-login.php just set user_login to GENERATE_CUSTOM_SEQ_USERNAME and hide the field using CSS.

See StackOverflow question for specific details: https://wordpress.stackexchange.com/questions/296101/auto-assign-sequence-base-username-while-registration