Good question. In the 17th and 18th century, yes, it seems the name on the stern of a ship include the article. But in the 19th century, this practice seems gradually abandoned (but many ships have the article on their stern during the Napoleonic era).
For exemple, models of the Musée national de la Marine in Paris :
Le Triomphant (ship of the line, 1809) : http://mnm.webmuseo.com/ws/musee-national-marine/app/file/download/M5026-2001-DE-0019-2.jpg?key=ae4d2ez8is4d3z3jjjd0wqp00htk8edlo
La Flore (frigate, 1806) : http://culturebox.francetvinfo.fr/sites/default/files/styles/article_view_full_main_image/public/assets/images/2014/06/marine-poupe.jpg?itok=N4stH7fl
L'Océan, 118-gun :
And l'Hermione today :