How do I assign custom names to ships?

[Inglonias]

Can I rename my vessels on a ship-by-ship basis? If so, how?

[Endless Galactica]

Select the ship. In the box where the ship name is listed, left click and overwrite it

[Ri0Rdian]

Or just enter the bases and ships windows, select the required ship and rename using the name box on the right. You don't need to know where the ships is nor click it to do so.