Yes. You should notify the Business Registration Office of the change of business address within one month from the date of change by submitting a written notification or a completed Form IRC3111A (pdf format).
The Companies Registry and the Inland Revenue Department (IRD) have jointly implemented an OPTIONAL ELECTRONIC one-stop notification service at the e-Registry for a company to report the change of registered office address also as a change of business address on its Business Registration Certificate. By using this electronic service, you may request the Registrar of Companies to notify the Commissioner of Inland Revenue on your behalf that the business address of your company as registered under the Business Registration Ordinance (Chapter 310 of the Laws of Hong Kong) has changed to the new address of your registered office with effect from the effective date of change as stated in the electronic Form NR1.
Normally, the IRD will send out your amended Business Registration Certificate by post on the next working day after registration of the electronic Form NR1 by the Companies Registry.