I've been asked the question of "Why is the ship called Iliad-07". And there is a method to my madness. It's a bit like the NASA convention in the early days of space exploration to have specific missions with goals, and each successive mission would get a number.

NASA had:

Mercury Crewed orbital flight 36
Gemini Crewed orbital flight, Extravehicular activity, Rendezvous and docking 12
Apollo Crewed lunar landing 17

The story is named after the Mission. The ship itself is Hull number IP034013. I-ISTO, P - Psyche Shipyards, 034 - Graving dock 34, 013 - Thirteenth hull produced serially. The Vessel's official name is the "SCV Arthur C. Clarke". The crew call her "Arty". SCV stands for Space Colony Vessel. The settlement calls itself "Clarkesvillie".

The Iliad project is the follow on to the [Epic of] Gilgamesh project. The projects are named after mythic journeys.

In the Epic of Gilgamesh, Gilgamesh would venture for 6 months at a time before returning home with treasures or commodities. The Vessels of the Gilgamesh project were designed to mine fuel from the Oort cloud surrounding the Solar system, and these trips would take 6 months even with a G drive.

The events in the Iliad, are at the end of 10 years, and feature a large construction project built from the parts of the ship that carried them there. The vessels of the Iliad project were designed to travel for decades under constant accelleration, and build remote remote outposts using the Vessel itself as the foundation for that colony.

After the colony constructs the infrastructure and line of communications to materials it needs, it would assemble a ship to return to Earth. These ships are project Odyssey.

This mission is Iliad-07, because there were 6 missions prior. See Timeline of Iliad 07