How to get user ID during registration and add it to a custom table

add_action( 'user_register', 'usermeta_update');

function usermeta_update( $user_id )

{ 
  
    add_action('woocommerce_created_customer', 'save_data', $user_id);

}

//save data
function save_data($customer_id)

{

    //First name field
    if (isset($_POST['billing_first_name'])) {
        update_user_meta($customer_id, 'first_name', sanitize_text_field($_POST['billing_first_name']));
        update_user_meta($customer_id, 'billing_first_name', sanitize_text_field($_POST['billing_first_name']));
    }

    //Last name field
    if (isset($_POST['billing_last_name'])) {
        update_user_meta($customer_id, 'last_name', sanitize_text_field($_POST['billing_last_name']));
        update_user_meta($customer_id, 'billing_last_name', sanitize_text_field($_POST['billing_last_name']));
    }
}

@Brady's answer is correct because WP-Members does use WP's function for inserting a new user, so that action does get called. And if you want flexibility and you are only using the new user's ID for all of it, that's a good approach.

But a secondary approach would be to use WP-Members' wpmem_post_register_data action. That action passes all of the user's registration data an array keyed by the field meta keys and it includes ID.

add_action( 'wpmem_post_register_data', 'my_reg_hook' );
function my_reg_hook( $fields ) {
    /* 
     * ID is available as $fields['ID']
     * Other fields are $fields['the_fields_meta_key']
     *
     * do your stuff here
     */
    return;
}

The documentation for the action has a list of fields that will be included in the array in addition to any custom fields that are in there by meta key:

https://rocketgeek.com/plugins/wp-members/docs/filter-hooks/wpmem_post_register_data/

Please take a look at user_register hook

This is fired when a new user is registered and conveniently passes you the user ID of the new user.

function function_name( $user_id )
{        
    /* do what you want to do with ID here */
}
add_action( 'user_register', 'function_name');