You can submit your application in person to the Travel Documents and Nationality (Application) Section or one of the Immigration Branch Offices. You are required the relevant supporting doucments (e.g. deed poll), you also have to copy your existing HKSAR passport. As the personal particulars in the passport should be identical to those shown on the Hong Kong permanent identity card, you are required to apply for amedment to the registered particulars at the Registration of Persons Office before submitting the application for amendment to the personal particulars in the passport.

Should the application be approved, the HKSAR Immigration Department will issue a new passport with amended personal particulars to you and the passport will be of the same validity with your existing passport. The application fee is HK$84. Or, you may apply for a new passport with 10-year or 5-year validity (depending on the age of applicant). The application fee for a passport with 10-year validity is HK$370 (32 pages) / HK$460 (48 pages) and 5-year validity is HK$185 (32 pages) / HK$230 (48 pages).--all from GovHK.