When pressing 'X' (or whatever key was assigned to spawning a new core), the dialog prompting the player to enter the new ship's name will always appear, regardless if the player has a shipcore in his/her inventory.
To reproduce:

1. Remove all ship-cores from your inventory
2. Attempt to spawn a new ship
3. Observe, as the dialog appears
4. Hit 'OK' in the dialog
5. Observe, as a message tells you, that you have no core element.