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