Hey psyco, you can't change the name of your ship but you can upgrade cannons, ram, and other weapons. Also you can customize the appearance with sails and wheel etc.
I would say this has been my best gaming experience for a long while. It's a fantastic adventure.
To get the most out of it play small parts of the main story, and do your own exploring.
When my ship was fairly weak I would watch the Brits and Spanish in big battles and finish of the damaged ships