I'm fairly certain that the ability to customize the name of your ship would be a welcome feature to most players. However, if it is somthing only you can see, what is really the point.
I propose this feature work similar to the pet naming feature in terms of how to go about actually setting the name of your ship. Just a simple option in the shipwright chest. With the obvious language filters in place to prevent abuse.
To actually make it mean somthing, I propose combining the island banner trigger with the audio trigger when looking at a ship with your spyglass.
Basically, when looking at a ship with your spyglass, if the ship is named, it triggers a small (possibly customizable?) banner, smaller than an island banner, to appear displaying the name of the ship. If implemented in this or similar way, it allows crews to build notoriety and fame in their region, should they choose to use the same name every time they set sail. It also could add to the cat and mouse of tracking a ship, if the quarry manages to give you the slip and make it to a shipwright to paint over the name before you catch sight of them again.
