I think including the word "The" in a vessel's name is a recent trend (probably within the last 50 years or so), IMHO, mostly due to the fact that as boating becomes something that more and more of the general public becomes involved in, the further from nautical tradition the sport moves. Traditionally, one would not name a boat "The Jane Doe" nor would you even use the word "the" when referring to the boat by name. You would say, for example, "I went aboard Jane Doe last night." (no pun intended
). But language is a dynamic thing and what was consider correct and acceptable 100 years ago is likely to be somewhat different now.
There are ocassions where the use of the word "The" in a boat name is proper. One that always sticks out in my mind is "The Nutmeg of Consolation" from the Aubrey/Maturin series by O'Brien.