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There is a legal answer to the question, and the answer is yes, it would continue to be the same ship, at least according to Lloyds of London.
In philosophical terms, also the same boat. It has continued to exit as something we would recognise as a ship throughout, and has not been modified, merely repaired.
What if I take all of the pieces that were removed, and put them back together? Would that be a different boat?
Yes
It would be a new boat, yes. The component parts are older, but it has existed as something we would consider a boat for a shorter amount of time.
Then, what if we took half the boat completely apart, and then pit it back together? Is it now a new or the old boat?
I remember my dad's car project, where an old Citroën was completely in pieces. That's not the same car, after he put it back together? (Not that he ever did)