I feel like Dragon is making a reference to the soul. Not sure if that is conjecture. The real thing that holds things to a name is form information, as has been stated (memes.) That is something that can be grasped even in a materialistic philosophy.
Note, I was not speaking of "soul" in the spiritual sense. There really isn't a different word that can describe things which are unrelated, but have the same effect of "personalizing" an object such as a computer, a car or a ship. For a person, this indeed is information and memes, the actual personality. For computers, it's the HD contents (hardware quirks can happen, but are rare, reinstalling the OS usually results in a "blank slate" without the usual glitches). However, for other things, it's various things that either appear over time or are inherent in the construction method. Those thing make a complex piece of technology unique, despite being made of mass produced parts.
Okay then, is it still the Ship of Theseus if you probably still have original planks on board but maybe have already replaced them all?
If you can't be sure of whether there are still original parts left, you can't be sure of that, either (the probabilities of either state are proportional to the average confidence level in it). If nobody knows for sure and there are no logs (with probabilities being 50-50), then this question can't, in fact, be answered for that particular vessel. If you want to be pedantic, you might assume a superposition of both states, but I'm not sure if doing it for the entire ship is a valid reasoning (works for particles, though).