The certificate of freedom is interesting. I guess she remained Sharkey in the convict records even though she was Mrs Herbert by then. I have ordered the death certificate. I think Sharkey was a reasonably common name in Ireland. There were several other convicts named Sharkey but no suggestion they were related.
No need to guess. The admin system was set up by NSW Governor Lachlan Macquarie in around 1810. Previous governors had been Royal Navy men. He was Army and Scottish born and taking over after a coup d'etat. He was born in Scotland, his wife was a Campbell, and his administrative decisions basically followed the Scottish tradition. So regardless of whether the female was transported under the sentence of a civil court or if she came as part of the household of a garrison force, or came free, whatever name she was known by when she landed was the name that was usually retained in the official records. Among his many admin systems, he set up the first system of BDM registrations, so that each quarter, his office received information that allowed him to notify Whitehall and receive funding based on the net per capita increase in the penal settlements' populations (free, came free, still under bond, born in the colony etc) under his administration.
JM