If you want your baby's surname on the birth certificate, the ONLY way to get it is to get a 'shortened' birth certificate, which is only available from the Admiralty office.
DS has a different surname from both DH and myself (traditional naming custom in DH's family) but the Aus embassy refused to accept his legally registered name from the standard birth cert, because it didn't appear on the cert. The HK registry will not put the surname on the standard certificate at all. It's not 'standard formating'. :eyesroll:
The embassy should be pretty used to HK birth certificates, and if your baby has either your husband's or your name, then it's pretty straight forward.