As of now, you may not change the name of your ship after creating it to it, however this is a planned feature in future iterations of the game. However, you can edit the name with the faction module.
After naming your ship, you may enter the core by targeting it with the mouse reticle and pressing [R]. Once you have done this, press [space] to enter build mode. In this mode, the player may press the " [WASD] and the [Q] and [E] keys to move forward, left, backwards, right, up, and down respectively. The player may edit around the ship core and place necessary blocks by using the left mouse button, and remove them with the right mouse button.
Even the most basic ships will require the following: a power supply, propulsion, protection and weapons . So, to start with, place power blocks on your ship. The bar on the bottom-right will fill up, meaning your ship is charging. Make sure to place thrusters on your ship. You will automatically use your power. Now your ship is ready for flight! The next thing you should add are weapons. All weapons currently correspond to specific controller blocks. Once you've placed some of these, hit [t] (this will open up the weapons menu), click on the weapons controller in the list and press a number on your keyboard to bind your weapons to that specific slot.
For more information and to get a proper layout on key bindings, please visit the image link below that is in printer format.