The HK birth certificate is indeed a strange thing. My husband had a huge argument with the officer at the birth registry because according to the traditions of the part of India he comes from the children take the father's first name as their last name. However, the birth registry insisted they could only do father's last name as child's last name (I heard that they might be open to mother's last name as an alternative but that's it). Finally, they said - oh but anyway we don't put the child's last name as such, only given name. Which is true, kind of. On the birth certificate there is only a space for given name and so my husband put the first and last name of his choice. However, on the sticker to immigration he recieved it had the father's last name as the child's last name and the two given names as first and middle name. So on some record somewhere in the birth registry that is the name, which annoys me.
Anyway, luckily as suggested by the birth registry, we were able to get our baby's passport issued through our consulate with the name of our choice and then the subsequent visa issued by immigration had the correct name as well.