Try to ensure billing company is unique when checking out or saving from myaccount.

wc-unique-billing.php

<?php

/**
 * Check for existing billing companies when updating my account data.
 *
 * @param WP_Error $errors Errors already added.
 * @param stdClass $user Current User data.
 */
function wc_myaccount_validate_billing_company( $errors, $user ) {

	$existing_billing_companies = wc_get_existing_billing_companies();

	if ( ! empty ( $existing_billing_companies ) ) {
		if ( in_array( esc_attr( stripslashes( $_POST['billing_company'] ) ), $existing_billing_companies, true ) ) {
			wc_add_notice( __( '<strong>Billing Company</strong> already exists.' ), 'error' );
		}
	}

}
add_action( 'woocommerce_save_account_details_errors', 'wc_myaccount_validate_billing_company', 10, 2 );

/**
 * Check for existing billing companies during the checkout process.
 */
function wc_checkout_validate_billing_company() {

	$existing_billing_companies = wc_get_existing_billing_companies();

	if ( ! empty ( $existing_billing_companies ) ) {
		if ( in_array( esc_attr( stripslashes( $_POST['billing_company'] ) ), $existing_billing_companies, true ) ) {
			wc_add_notice( __( '<strong>Billing Company</strong> already exists.' ), 'error' );
		}
	}
}
add_action( 'woocommerce_checkout_process', 'wc_checkout_validate_billing_company' );

/**
 * Check the DB for existing billing company values.
 *
 * @return array|void
 */
function wc_get_existing_billing_companies() {
	$existing_billing_companies = get_transient( 'wc_unique_billing_companies' );

	if ( ! $existing_billing_companies ) {
		global $wpdb;
		$existing_billing_companies = $wpdb->get_results(
			$wpdb->prepare(
				"SELECT meta_value FROM {$wpdb->postmeta} WHERE meta_key = %s",
				'_billing_company'
			),
			ARRAY_A
		);

		if ( ! empty( $existing_billing_companies ) && is_wp_error( $existing_billing_companies ) ) {
			wc_get_logger()->warning( sprintf( 'WordPress error: %s', implode( ' / ', $existing_billing_companies->get_error_messages() ) ), [] );
			wc_add_notice( __( 'Something went wrong, please contact a site administrator or try again.' ), 'error' );

			return;
		}

		set_transient( 'wc_unique_billing_companies', $existing_billing_companies );
	}

	return $existing_billing_companies;
}