As long as you are not travelling to/from Mainland China using a Home Return Permit or to/from Taiwan using a Taiwan travel permit, then you'll have no problems.

When travelling to/from Mainland China or to/from Taiwan and using the above mentioned documents, you need to make sure that the English equivalent of all the Chinese characters on your travel document is reflected on your ticket.

If one of these components is missing, then your "Chinese name" is not complete.

No need to worry about missing a middle name if you are not using a HKSAR, Macau SAR, ROC or PRC travel document where there is a Chinese character equivalent to your name.